Sharing in a Ratio

Find the value of one part from the total number of parts.

Find the number in one part, then use the red part of the ratio.

Find one part, then take the number of parts belonging to Ava.

Tom has the second number of parts in the stated ratio.

The longer piece has three of the four equal parts.

Find one part using the total of both ratio numbers, then multiply by the parts for each colour.

Part (a)

1. There are 3+5=8 parts, so one part contains 48\div8=6 counters.
2. Red counters: 3\times6=18.

Part (b)

1. Blue counters have 5 parts of 6 counters each.
2. 5\times6=30. Check: 18+30=48.

Add all three ratio numbers to find the total number of parts.

Part (a)

1. There are 1+3+4=8 parts, so one part is worth 96\div8=12 pounds.
2. Rea has one part and receives £12.

Part (b)

1. One part is worth 96\div8=12 pounds.
2. Sam has 3 parts and receives 3\times12=36 pounds, or £36.

Part (c)

1. One part is worth 96\div8=12 pounds.
2. Tali has 4 parts and receives 4\times12=48 pounds, or £48.
3. Check: 12+36+48=96 pounds.

The denominator counts all parts, not just the orange parts.

1. Apple sweets take 7 of the 2+7=9 parts.
2. The fraction is \frac79.

The total volume represents all five parts of the mixture.

1. Total parts: 2+3=5.
2. One part is 7.5\div5=1.5 litres.
3. Red paint is 2\times1.5=3 litres.

You can simplify the ratio first, or work directly with all sixteen parts.

1. There are 6+10=16 parts, so one part is worth 80\div16=5 pounds.
2. The larger share has 10 parts: 10\times5=50 pounds, or £50.
3. Check: the smaller share is 6\times5=30 pounds, and 30+50=80.

Find the two shares and subtract, or find how many parts the difference represents.

1. The total is 2+5=7 parts, so one part is worth 84\div7=12 pounds.
2. Hari has 5-2=3 more parts than Zoe.
3. The difference is 3\times12=36 pounds, or £36.

Convert the total to millilitres, then share it between all eight parts.

1. 2.4 litres is 2400 ml.
2. Total parts: 1+7=8. One part is 2400\div8=300 ml.
3. Juice is one part, so there are 300 ml of juice.

Find Lara’s share before subtracting her spending.

1. Total parts: 2+5=7. Each is worth 63\div7=9 pounds.
2. Lara receives 5\times9=45 pounds.
3. She has 45-18=27 pounds left, or £27.

Find the blue group before applying the fraction to that group.

1. There are 5+4=9 parts, so one part is 36\div9=4 mugs.
2. There are 4\times4=16 blue mugs.
3. Chipped blue mugs: 16\div4=4.
4. Blue mugs that are not chipped: 16-4=12.

Find the money left after expenses before dividing it in the ratio.

1. Money available to share: 210-30=180 pounds.
2. There are 4+5=9 parts. One part is worth 180\div9=20 pounds.
3. The smaller share is 4\times20=80 pounds, or £80.

Use Isla’s share to find Noah’s share, then calculate each person’s saving.

1. Isla’s 5 parts are worth £35, so one part is worth 35\div5=7 pounds.
2. Noah receives 2\times7=14 pounds. He saves 14\div2=7 pounds.
3. Isla saves 35\div5\times3=21 pounds.
4. They save 7+21=28 pounds altogether.

The difference between the ratio numbers tells you how many parts £36 represents.

1. The difference is 7-4=3 parts.
2. One part is worth 36\div3=12 pounds.
3. The total has 4+7=11 parts, worth 11\times12=132 pounds, or £132.

For each ingredient, find the greatest mass that one ratio part could have. All three ingredients must be available in the correct proportions.

1. Sunflower seeds allow one part to be at most 300\div3=100 g.
2. Sesame seeds allow one part to be at most 180\div2=90 g.
3. Pumpkin seeds allow one part to be at most 350\div5=70 g.
4. The smallest limit is 70 g, so the greatest total is (3+2+5)\times70=700 g.
5. This uses 210 g of sunflower seeds, 140 g of sesame seeds and 350 g of pumpkin seeds. All three amounts are available; making more would need extra pumpkin seeds.

Find the difference between the shares. Giving £1 across reduces that difference by £2.

1. Total parts: 4+5=9. One part is worth 126\div9=14 pounds.
2. Ada receives 4\times14=56 pounds; Bilal receives 5\times14=70 pounds.
3. The difference is 70-56=14 pounds. A transfer increases one share and decreases the other by the same amount.
4. Transfer half the difference: 14\div2=7 pounds. Check: 56+7=70-7=63.

Find each person's first share. The total is still £180 after the gift, so share £180 again in the new ratio.

1. First shares: 4+3+2=9 parts, and 180\div9=20, so Amy has £80, Ben £60 and Cal £40.
2. After the gift the total is still £180: 5+6+7=18 parts, and 180\div18=10, so Amy has £50, Ben £60 and Cal £70.
3. Ben still has £60, as he should. Cal went from £40 to £70.
4. Amy gave Cal 70-40=£30 (and Amy went from £80 to £50, which agrees).