# Number - Improper Fractions and Mixed Numbers

**Question 1**

Classify the following as a proper fraction or an improper fraction (also known as top-heavy) or a mixed number:

a) $\frac13$

a
Proper Fraction

Question ID: 10080010010

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s
As the numerator is less than the denominator this fraction is proper

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v

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b) $\frac52$

a
Improper Fraction

Question ID: 10080010020

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s
As the numerator is more than the denominator this fraction is improper

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v

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c) $1\frac14$

a
Mixed Number

Question ID: 10080010030

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s
As this term contains both a whole number and a fraction this is a mixed number

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v

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d) $\frac67$

a
Proper Fraction

Question ID: 10080010040

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s
As the numerator is less than the denominator this fraction is proper

Question ID: 10080010040

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v

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e) $\frac76$

a
Improper Fraction

Question ID: 10080010050

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s
As the numerator is more than the denominator this fraction is improper

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v

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f) $2\frac58$

a
Mixed Number

Question ID: 10080010060

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s
As this term contains both a whole number and a fraction this is a mixed number

Question ID: 10080010060

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v

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g) $8\frac{3}{16}$

a
Mixed Number

Question ID: 10080010070

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s
As this term contains both a whole number and a fraction this is a mixed number

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v

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h) $\frac{99}{100}$

a
Proper Fraction

Question ID: 10080010080

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s
As the numerator is less than the denominator this fraction is proper

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i) $\frac{20}{13}$

a
Improper Fraction

Question ID: 10080010090

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s
As the numerator is more than the denominator this fraction is improper

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v

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j) $506\frac{23}{40}$

a
Mixed Number

Question ID: 10080010100

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s
As this term contains both a whole number and a fraction this is a mixed number

Question ID: 10080010100

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v

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k) $\frac{89}{15}$

a
Improper Fraction

Question ID: 10080010110

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s
As the numerator is more than the denominator this fraction is improper

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v

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**Question 2**

Convert the following improper fractions to mixed numbers

a) $\frac52$

a
$2\frac12$

Question ID: 10080020010

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s
To convert $\frac52$ into a mixed number, divide the numerator by the denominator.

$5\div2=2\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $2\frac12$

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b) $\frac72$

a
$3\frac12$

Question ID: 10080020020

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s
To convert $\frac72$ into a mixed number, divide the numerator by the denominator.

$7\div2=3\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $3\frac12$

Question ID: 10080020020

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v

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c) $\frac{11}{2}$

a
$5\frac12$

Question ID: 10080020030

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s
To convert $\frac{11}{2}$ into a mixed number, divide the numerator by the denominator.

$11\div2=5\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $5\frac12$

Question ID: 10080020030

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v

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d) $\frac43$

a
$1\frac13$

Question ID: 10080020040

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s
To convert $\frac{4}{3}$ into a mixed number, divide the numerator by the denominator.

$4\div3=1\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac13$ and the whole number sits out front to give $1\frac13$

Question ID: 10080020040

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v

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e) $\frac83$

a
$2\frac23$

Question ID: 10080020050

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s

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f) $\frac54$

a
$1\frac14$

Question ID: 10080020060

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g) $\frac74$

a
$1\frac34$

Question ID: 10080020070

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h) $\frac85$

a
$1\frac35$

Question ID: 10080020080

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i) $\frac{13}{5}$

a
$2\frac35$

Question ID: 10080020090

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s
To convert $\frac{13}{5}$ into a mixed number, divide the numerator by the denominator.

$13\div5=2\text{ remainder }3$

The remainder still 'needs to be divided' so this is expressed as $\frac35$ and the whole number sits out front to give $2\frac35$

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j) $\frac{11}{6}$

a
$1\frac56$

Question ID: 10080020100

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k) $\frac{15}{7}$

a
$1\frac17$

Question ID: 10080020110

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l) $\frac{20}{9}$

a
$2\frac29$

Question ID: 10080020120

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m) $\frac{44}{7}$

a
$6\frac27$

Question ID: 10080020130

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n) $\frac{27}{10}$

a
$2\frac{7}{10}$

Question ID: 10080020140

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o) $\frac{34}{11}$

a
$3\frac{1}{11}$

Question ID: 10080020150

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p) $\frac{17}{12}$

a
$1\frac{5}{12}$

Question ID: 10080020160

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q) $\frac{55}{12}$

a
$4\frac{7}{12}$

Question ID: 10080020170

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r) $\frac{89}{7}$

a
$12\frac57$

Question ID: 10080020180

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s
To convert $\frac{89}{7}$ into a mixed number, divide the numerator by the denominator.

$89\div7=12\text{ remainder }5$

The remainder still 'needs to be divided' so this is expressed as $\frac57$ and the whole number sits out front to give $12\frac57$

Question ID: 10080020180

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s) $\frac{145}{11}$

a
$13\frac{2}{11}$

Question ID: 10080020190

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t) $\frac{245}{12}$

a
$20\frac{5}{12}$

Question ID: 10080020200

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**Question 3**

Convert the following mixed numbers to improper fractions

a) $2\frac34$

a
$\frac{11}{4}$

Question ID: 10080030010

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To convert $2\frac34$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}2\times4&=8\\8+3&=11\\\text{therefore }&\frac{11}{4}\end{align}$

Question ID: 10080030010

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b) $3\frac25$

a
$\frac{17}{5}$

Question ID: 10080030020

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To convert $3\frac25$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}3\times5&=15\\15+2&=17\\\text{therefore }&\frac{17}{5}\end{align}$

Question ID: 10080030020

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c) $4\frac13$

a
$\frac{13}{3}$

Question ID: 10080030030

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d) $1\frac12$

a
$\frac32$

Question ID: 10080030040

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To convert $1\frac12$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}1\times2&=2\\2+1&=3\\\text{therefore }&\frac{3}{2}\end{align}$

Question ID: 10080030040

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e) $1\frac16$

a
$\frac76$

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f) $2\frac59$

a
$\frac{23}{9}$

Question ID: 10080030060

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g) $5\frac15$

a
$\frac{26}{5}$

Question ID: 10080030070

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h) $6\frac34$

a
$\frac{27}{4}$

Question ID: 10080030080

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Question ID: 10080030080

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i) $7\frac13$

a
$\frac{22}{3}$

Question ID: 10080030090

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Question ID: 10080030090

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j) $4\frac45$

a
$\frac{24}{5}$

Question ID: 10080030100

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k) $8\frac23$

a
$\frac{26}{3}$

Question ID: 10080030110

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l) $10\frac79$

a
$\frac{97}{9}$

Question ID: 10080030120

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m) $8\frac57$

a
$\frac{61}{7}$

Question ID: 10080030130

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n) $9\frac59$

a
$\frac{86}{9}$

Question ID: 10080030140

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o) $12\frac35$

a
$\frac{63}{5}$

Question ID: 10080030150

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p) $8\frac89$

a
$\frac{80}{9}$

Question ID: 10080030160

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q) $4\frac{11}{15}$

a
$\frac{71}{15}$

Question ID: 10080030170

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r) $11\frac{4}{7}$

a
$\frac{81}{7}$

Question ID: 10080030180

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s) $12\frac{5}{11}$

a
$\frac{137}{11}$

Question ID: 10080030190

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Question ID: 10080030190

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t) $13\frac34$

a
$\frac{55}{4}$

Question ID: 10080030200

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**Question 4**

By turning both into mixed numbers, find which fraction is bigger

a) $2\frac12$ and $\frac32$

a
$2\frac12$ is bigger

Question ID: 10080040010

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$\frac32=1\frac12$ compare this to $2\frac12$, showing that $2\frac12$ is bigger.

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b) $3\frac14$ and $\frac{15}{4}$

a
$\frac{15}{4}$ is bigger

Question ID: 10080040020

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$\frac{15}{4}=3\frac34$ compare this to $3\frac14$, showing that $\frac{15}{4}$ is bigger.

Question ID: 10080040020

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c) $2\frac47$ and $\frac{13}{6}$

a
$2\frac47$ is bigger

Question ID: 10080040030

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d) $4\frac25$ and $\frac{44}{9}$

a
$\frac{44}{9}$ is bigger

Question ID: 10080040040

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e) $8\frac13$ and $\frac{26}{3}$

a
$\frac{26}{3}$ is bigger

Question ID: 10080040050

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f) $4\frac{7}{10}$ and $\frac{56}{11}$

a
$\frac{56}{11}$ is bigger

Question ID: 10080040060

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g) $4\frac{12}{13}$ and $\frac{63}{13}$

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$4\frac{12}{13}$ is bigger

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h) $12\frac{5}{13}$ and $\frac{160}{13}$

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$12\frac{5}{13}$ is bigger

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**Question 1**

Classify the following as a proper fraction or an improper fraction (also known as top-heavy) or a mixed number:

a) $\frac13$

b) $\frac52$

c) $1\frac14$

d) $\frac67$

e) $\frac76$

f) $2\frac58$

g) $8\frac{3}{16}$

h) $\frac{99}{100}$

i) $\frac{20}{13}$

j) $506\frac{23}{40}$

k) $\frac{89}{15}$

**Question 2**

Convert the following improper fractions to mixed numbers

a) $\frac52$

b) $\frac72$

c) $\frac{11}{2}$

d) $\frac43$

e) $\frac83$

f) $\frac54$

g) $\frac74$

h) $\frac85$

i) $\frac{13}{5}$

j) $\frac{11}{6}$

k) $\frac{15}{7}$

l) $\frac{20}{9}$

m) $\frac{44}{7}$

n) $\frac{27}{10}$

o) $\frac{34}{11}$

p) $\frac{17}{12}$

q) $\frac{55}{12}$

r) $\frac{89}{7}$

s) $\frac{145}{11}$

t) $\frac{245}{12}$

**Question 3**

Convert the following mixed numbers to improper fractions

a) $2\frac34$

b) $3\frac25$

c) $4\frac13$

d) $1\frac12$

e) $1\frac16$

f) $2\frac59$

g) $5\frac15$

h) $6\frac34$

i) $7\frac13$

j) $4\frac45$

k) $8\frac23$

l) $10\frac79$

m) $8\frac57$

n) $9\frac59$

o) $12\frac35$

p) $8\frac89$

q) $4\frac{11}{15}$

r) $11\frac{4}{7}$

s) $12\frac{5}{11}$

t) $13\frac34$

**Question 4**

By turning both into mixed numbers, find which fraction is bigger

a) $2\frac12$ and $\frac32$

b) $3\frac14$ and $\frac{15}{4}$

c) $2\frac47$ and $\frac{13}{6}$

d) $4\frac25$ and $\frac{44}{9}$

e) $8\frac13$ and $\frac{26}{3}$

f) $4\frac{7}{10}$ and $\frac{56}{11}$

g) $4\frac{12}{13}$ and $\frac{63}{13}$

h) $12\frac{5}{13}$ and $\frac{160}{13}$

__Answers__

**Question 1**

a) Proper Fraction

b) Improper Fraction

c) Mixed Number

d) Proper Fraction

e) Improper Fraction

f) Mixed Number

g) Mixed Number

h) Proper Fraction

i) Improper Fraction

j) Mixed Number

k) Improper Fraction

**Question 2**

a) $2\frac12$

b) $3\frac12$

c) $5\frac12$

d) $1\frac13$

e) $2\frac23$

f) $1\frac14$

g) $1\frac34$

h) $1\frac35$

i) $2\frac35$

j) $1\frac56$

k) $1\frac17$

l) $2\frac29$

m) $6\frac27$

n) $2\frac{7}{10}$

o) $3\frac{1}{11}$

p) $1\frac{5}{12}$

q) $4\frac{7}{12}$

r) $12\frac57$

s) $13\frac{2}{11}$

t) $20\frac{5}{12}$

**Question 3**

a) $\frac{11}{4}$

b) $\frac{17}{5}$

c) $\frac{13}{3}$

d) $\frac32$

e) $\frac76$

f) $\frac{23}{9}$

g) $\frac{26}{5}$

h) $\frac{27}{4}$

i) $\frac{22}{3}$

j) $\frac{24}{5}$

k) $\frac{26}{3}$

l) $\frac{97}{9}$

m) $\frac{61}{7}$

n) $\frac{86}{9}$

o) $\frac{63}{5}$

p) $\frac{80}{9}$

q) $\frac{71}{15}$

r) $\frac{81}{7}$

s) $\frac{137}{11}$

t) $\frac{55}{4}$

**Question 4**

a) $2\frac12$ is bigger

b) $\frac{15}{4}$ is bigger

c) $2\frac47$ is bigger

d) $\frac{44}{9}$ is bigger

e) $\frac{26}{3}$ is bigger

f) $\frac{56}{11}$ is bigger

g) $4\frac{12}{13}$ is bigger

h) $12\frac{5}{13}$ is bigger

**Question 1**

Classify the following as a proper fraction or an improper fraction (also known as top-heavy) or a mixed number:

a) $\frac13$

b) $\frac52$

c) $1\frac14$

d) $\frac67$

e) $\frac76$

f) $2\frac58$

g) $8\frac{3}{16}$

h) $\frac{99}{100}$

i) $\frac{20}{13}$

j) $506\frac{23}{40}$

k) $\frac{89}{15}$

**Question 2**

Convert the following improper fractions to mixed numbers

a) $\frac52$

b) $\frac72$

c) $\frac{11}{2}$

d) $\frac43$

e) $\frac83$

f) $\frac54$

g) $\frac74$

h) $\frac85$

i) $\frac{13}{5}$

j) $\frac{11}{6}$

k) $\frac{15}{7}$

l) $\frac{20}{9}$

m) $\frac{44}{7}$

n) $\frac{27}{10}$

o) $\frac{34}{11}$

p) $\frac{17}{12}$

q) $\frac{55}{12}$

r) $\frac{89}{7}$

s) $\frac{145}{11}$

t) $\frac{245}{12}$

**Question 3**

Convert the following mixed numbers to improper fractions

a) $2\frac34$

b) $3\frac25$

c) $4\frac13$

d) $1\frac12$

e) $1\frac16$

f) $2\frac59$

g) $5\frac15$

h) $6\frac34$

i) $7\frac13$

j) $4\frac45$

k) $8\frac23$

l) $10\frac79$

m) $8\frac57$

n) $9\frac59$

o) $12\frac35$

p) $8\frac89$

q) $4\frac{11}{15}$

r) $11\frac{4}{7}$

s) $12\frac{5}{11}$

t) $13\frac34$

**Question 4**

By turning both into mixed numbers, find which fraction is bigger

a) $2\frac12$ and $\frac32$

b) $3\frac14$ and $\frac{15}{4}$

c) $2\frac47$ and $\frac{13}{6}$

d) $4\frac25$ and $\frac{44}{9}$

e) $8\frac13$ and $\frac{26}{3}$

f) $4\frac{7}{10}$ and $\frac{56}{11}$

g) $4\frac{12}{13}$ and $\frac{63}{13}$

h) $12\frac{5}{13}$ and $\frac{160}{13}$

__Answers__

**Question 1**

a) Proper Fraction

b) Improper Fraction

c) Mixed Number

d) Proper Fraction

e) Improper Fraction

f) Mixed Number

g) Mixed Number

h) Proper Fraction

i) Improper Fraction

j) Mixed Number

k) Improper Fraction

**Question 2**

a) $2\frac12$

b) $3\frac12$

c) $5\frac12$

d) $1\frac13$

e) $2\frac23$

f) $1\frac14$

g) $1\frac34$

h) $1\frac35$

i) $2\frac35$

j) $1\frac56$

k) $1\frac17$

l) $2\frac29$

m) $6\frac27$

n) $2\frac{7}{10}$

o) $3\frac{1}{11}$

p) $1\frac{5}{12}$

q) $4\frac{7}{12}$

r) $12\frac57$

s) $13\frac{2}{11}$

t) $20\frac{5}{12}$

**Question 3**

a) $\frac{11}{4}$

b) $\frac{17}{5}$

c) $\frac{13}{3}$

d) $\frac32$

e) $\frac76$

f) $\frac{23}{9}$

g) $\frac{26}{5}$

h) $\frac{27}{4}$

i) $\frac{22}{3}$

j) $\frac{24}{5}$

k) $\frac{26}{3}$

l) $\frac{97}{9}$

m) $\frac{61}{7}$

n) $\frac{86}{9}$

o) $\frac{63}{5}$

p) $\frac{80}{9}$

q) $\frac{71}{15}$

r) $\frac{81}{7}$

s) $\frac{137}{11}$

t) $\frac{55}{4}$

**Question 4**

a) $2\frac12$ is bigger

b) $\frac{15}{4}$ is bigger

c) $2\frac47$ is bigger

d) $\frac{44}{9}$ is bigger

e) $\frac{26}{3}$ is bigger

f) $\frac{56}{11}$ is bigger

g) $4\frac{12}{13}$ is bigger

h) $12\frac{5}{13}$ is bigger

__Solutions__

**Question 1**

a) As the numerator is less than the denominator this fraction is proper

b) As the numerator is more than the denominator this fraction is improper

c) As this term contains both a whole number and a fraction this is a mixed number

d) As the numerator is less than the denominator this fraction is proper

e) As the numerator is more than the denominator this fraction is improper

f) As this term contains both a whole number and a fraction this is a mixed number

g) As this term contains both a whole number and a fraction this is a mixed number

h) As the numerator is less than the denominator this fraction is proper

i) As the numerator is more than the denominator this fraction is improper

j) As this term contains both a whole number and a fraction this is a mixed number

k) As the numerator is more than the denominator this fraction is improper

**Question 2**

a) To convert $\frac52$ into a mixed number, divide the numerator by the denominator.

$5\div2=2\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $2\frac12$

b) To convert $\frac72$ into a mixed number, divide the numerator by the denominator.

$7\div2=3\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $3\frac12$

c) To convert $\frac{11}{2}$ into a mixed number, divide the numerator by the denominator.

$11\div2=5\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac12$ and the whole number sits out front to give $5\frac12$

d) To convert $\frac{4}{3}$ into a mixed number, divide the numerator by the denominator.

$4\div3=1\text{ remainder }1$

The remainder still 'needs to be divided' so this is expressed as $\frac13$ and the whole number sits out front to give $1\frac13$

e)

f)

g)

h)

i) To convert $\frac{13}{5}$ into a mixed number, divide the numerator by the denominator.

$13\div5=2\text{ remainder }3$

The remainder still 'needs to be divided' so this is expressed as $\frac35$ and the whole number sits out front to give $2\frac35$

j)

k)

l)

m)

n)

o)

p)

q)

r) To convert $\frac{89}{7}$ into a mixed number, divide the numerator by the denominator.

$89\div7=12\text{ remainder }5$

The remainder still 'needs to be divided' so this is expressed as $\frac57$ and the whole number sits out front to give $12\frac57$

s)

t)

**Question 3**

a) To convert $2\frac34$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}2\times4&=8\\8+3&=11\\\text{therefore }&\frac{11}{4}\end{align}$

b) To convert $3\frac25$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}3\times5&=15\\15+2&=17\\\text{therefore }&\frac{17}{5}\end{align}$

c)

d) To convert $1\frac12$ into an improper fraction, multiply the whole number by the denominator and add the numerator. Write the result above the original denominator.

$\begin{align}1\times2&=2\\2+1&=3\\\text{therefore }&\frac{3}{2}\end{align}$

e)

f)

g)

h)

i)

j)

k)

l)

m)

n)

o)

p)

q)

r)

s)

t)

**Question 4**

a) $\frac32=1\frac12$ compare this to $2\frac12$, showing that $2\frac12$ is bigger.

b) $\frac{15}{4}=3\frac34$ compare this to $3\frac14$, showing that $\frac{15}{4}$ is bigger.

c)

d)

e)

f)

g)

h)