Connected ideas

Bar models

Connect fractions, ratio, percentages and equations.

Predict, test and explain

Step 1 of 3

Predict

If 3x + 24 = 60, what is x?

35×60=36\frac{3}{5}\times60=36
Whole 60, fraction model
whole=60\text{whole}=60
selected=36\text{selected}=36
remaining=24\text{remaining}=24
one equal part=12\text{one equal part}=12

Scroll the diagram sideways to see every label.

36+24=6036+24=60

All parts refer to the same whole and have equal value.

InvestigateHow can the same whole be described as a fraction, a ratio and a percentage?

Explore and compare

Compare the starting fraction, ratio and percentage. Predict whether they select the same amount.

Try it in the simulation. Change one thing at a time.

Hint

Keep the whole at 60. Compare 3/5, ratio 3 : 2 and 60%. Then try the equation 3x + 24 = 60.

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Hints, self-check and connections
Try a self-check

Fixed values, separate from the diagram controls.

Share 84 in the ratio 2 : 5.

A:B=2:5A:B=2:5

Hint

Count all seven equal parts first.

Reveal answer

Each part is 12. Two parts make 24 and five parts make 60.

A=24,B=60A=24,\quad B=60

Build an explanation

Hint 1

Identify the whole before splitting it into parts.

Hint 2

Equal-sized parts have equal values. Divide the whole by the number of equal parts.

Hint 3

For an equation, remove the added amount before dividing what remains between the x-parts.

Worked example

This example uses fixed values, separate from the diagram controls.

Share 60 in the ratio 3 : 2.

  1. There are 3 + 2 = 5 equal parts in the whole.
  2. Each part is 60 ÷ 5 = 12.
  3. The first share is 3 × 12 = 36; the second is 2 × 12 = 24.

Answer: The shares are 36 and 24. The first share is also 3/5 or 60% of the whole.

Connect this idea

Watch out: The denominator counts parts of the whole; a ratio compares the two groups. In 3 : 2, the first group is 3/5 of the whole, not 3/2.