Ratios, equivalent groups and sharing

Red counters

\(\displaystyle 6\)

Blue counters

\(\displaystyle 10\)

Which count should appear first when comparing blue counters to red counters?

A ratio compares quantities in order

A ratio written with a colon compares quantities in the stated order

This means six red counters for every ten blue counters in this collection

Reversing the named categories reverses the ratio terms

When asked for actual counts, write those counts rather than simplifying them. Later tasks explicitly ask for simplest form

Write the two actual counts

A collection contains red and blue counters

The table includes every recorded item once, in exactly one category

Write the ratio of red to blue. Use the actual counts; do not simplify

The first term uses red: \(6\)

The second term uses blue: \(10\)

Write the actual counts in the requested order

Follow the named order instead of the table order

Use one ordered term for each category

A ratio can compare three quantities. Keep each count beside the correct named category

If the comparison changes to green, red, then blue, reorder the counts to match

The categories have not changed their counts. Only the requested order has changed

Write three counts in a new order

A part-to-whole comparison includes every category

A part-to-part ratio compares two selected groups. A part-to-whole ratio compares one selected group with the total, including that selected group

Six red, nine blue and five green counters make twenty counters altogether

Do not omit the red counters when finding the whole

Include the selected part in the total

Divide every term by the same common factor

Equivalent ratios describe the same relative quantities. Divide every term by the same positive factor to make an equivalent ratio

In simplest whole-number form, the terms have no common factor greater than one

The ratio two to three describes proportions, not necessarily a collection with only five items

Subtracting the same amount from each term generally does not preserve the ratio

Use the highest common factor

Write the simplest whole-number ratio

The HCF of all 2 terms is 6. Divide every term by it

No common factor greater than one remains. The ratio in simplest form is

Find the simplest whole-number ratio

Simplify all three terms together

Write the simplest whole-number ratio

The HCF of all 3 terms is 4. Divide every term by it

No common factor greater than one remains. The ratio in simplest form is

Use one common divisor for the entire ratio

Scale every term by the same factor

Multiplying every ratio term by the same positive number preserves the comparison

To find a missing term, use the known corresponding terms to find the scale factor

Two becomes eight by multiplying by four, so three also multiplies by four

Adding six to each term would give eight to nine, which is not equivalent to two to three

Find the common scale factor

Find the missing term

Divide the known target term by its corresponding term in the complete ratio

Apply this multiplier to the term corresponding to x

Substitute the missing term to check the completed ratios

Scale the missing first term

Keep a three-part comparison equivalent

The red-to-blue ratio is always two to three. Change the number of equal groups and compare the counts with the total

At four equal groups, which statement is correct?

Convert a part-to-part ratio to fractions of the total

In a two-to-three ratio, the whole contains five equal ratio parts

The first group receives two of the five parts and the second group receives three of them

Two thirds compares the first group with the second group. It is not the first group as a fraction of the whole

Use the sum of the terms as the denominator

A group of 50 volunteers is divided into teams in the ratio 2:3

Read the ratio in this order: first team, second team

What fraction of the total goes to the first team? Give a fraction in simplest form

Add every ratio term to count all equal parts in the whole

The first team has 2 of these equal parts

No common factor greater than one remains in the numerator and denominator

The denominator is the sum of the ratio terms, not another individual term

Find the second share as a fraction of the whole

Include all three terms in the whole

A one-to-one-to-two ratio has four equal parts in total

The first two groups each receive one quarter, and the third receives one half

Equal ratio terms represent equal shares and are allowed

Simplify a three-part share fraction

Find one equal part before each whole share

To divide sixty in the ratio two to three, first count the equal parts

Divide the total by five to find one equal part

Then multiply the one-part value by each ratio term

Check both the total and the ratio

Find the value of one ratio part

A group of 60 volunteers is divided into teams in the ratio 2:3

Read the ratio in this order: first team, second team

Find the value of one equal part in volunteers

Find the total number of parts

Find the value of one part

This is the value of one equal ratio part. A share contains as many of these parts as its ratio term specifies

Distinguish one part from an entire share

Allocate both shares in order

A group of 60 volunteers is divided into teams in the ratio 2:3

Read the ratio in this order: red team, blue team

Find the number of volunteers in each team

Find the total number of parts

Find the value of one part

Find each share

The red team has 2 equal parts

The blue team has 3 equal parts

Check that the shares add to the total

The shares add to the total and follow the ratio in the stated order

Find both shares and check their sum

Share a total in three parts

A group of 90 volunteers is divided into teams in the ratio 1:2:3

Read the ratio in this order: red team, blue team, green team

Find the number of volunteers in each team

Find the total number of parts

Find the value of one part

Find each share

The red team has 1 equal part

The blue team has 2 equal parts

The green team has 3 equal parts

Check that the shares add to the total

The shares add to the total and follow the ratio in the stated order

Use the total of all three ratio terms

Equal ratio terms receive equal shares

Ratio

\(\displaystyle 2:3:4\)

Total

\(\displaystyle 90\)

A total of ninety is shared in the ratio shown. Which calculation finds one equal ratio part?

Clear decimal places using one shared scale

A ratio may contain decimal terms. Multiply every term by the same power of ten to obtain whole-number terms

Scaling only one term would change the comparison

Once both terms are whole numbers, divide by their highest common factor

Simplify a decimal ratio

Use the same unit before simplifying a measurement ratio

Two metres and fifty centimetres are not in a two-to-fifty ratio, because the units differ

Convert to a common unit first, then simplify the numerical ratio

The conversion uses one metre equal to one hundred centimetres

Convert metres to centimetres first

Divide a measured length

Distinguish one part to four parts from one part in four

A blend with one part of a first component for every four parts of a second component has five equal parts altogether

The first component is one fifth of the total blend, not one quarter

For a fifteen-litre blend, one equal part is three litres

This mathematical model assumes the component volumes add to the stated total

Share the stated total blend

Keep order, equal parts and the whole visible

A ratio is ordered. Match each term to its named category, and follow whether the task asks for actual counts or simplest form

Multiply or divide all terms by the same positive factor to keep a ratio equivalent

For a fraction of the whole, divide the selected ratio term by the sum of all terms

For sharing, divide the total quantity by the total number of equal parts, then multiply by each term

Convert measurements to matching units before comparing, and check that all shares sum to the stated total