Dividing a quantity in a given ratio

Sharing an amount in a given ratio by finding the value of one part, and finding a total from one share.

Find one part

Example 1●

Divide $\$350$ in the ratio $3 : 4$.

$3 + 4 = 7$ parts. One part $= 350 \div 7 = 50$.

Shares: $3 \times 50 = \$150$ and $4 \times 50 = \$200$.

Example 2●●

Concrete mixes cement, sand and gravel in the ratio $1 : 2 : 4$. How much sand is in $210$ kg of concrete?

$7$ parts, so one part $= 30$ kg.

Sand $= 2 \times 30 = 60$ kg.

Example 3●●

Prize money is shared in the ratio $5 : 3$. The smaller share is $\$240$. Find the total.

$3$ parts $= 240$, so one part $= 80$.

Total $= 8 \times 80 = \$640$.

Flashcards

First step to share in a ratio

Add the parts.

$$60$ in ratio $1 : 2$

$\$20$ and $\$40$

Check your shares

They add to the total.

Practice

Divide $\$350$ in the ratio $3 : 4$. Enter both shares.
Cement : sand : gravel $= 1 : 2 : 4$. How many kg of sand in $210$ kg?
Shared $5 : 3$, the smaller share is $\$240$. Find the total.
Divide $\$60$ in the ratio $1 : 2$.
Boys : girls $= 4 : 5$ in a group of $81$. How many girls?
Juice and water are mixed $1 : 4$. How much juice is in $75$ mL of drink?
Angles of a triangle are in the ratio $1 : 2 : 7$. Find the middle-sized angle in degrees.
Red : blue $= 3 : 5$. There are $20$ blue. How many red?