Proportion - Recipes and the Unitary Method

Compare the number of portions, then change the rice by the same factor.

Compare 8 people with 4 people.

You want half as many flapjacks.

Share the total amount equally between the five smoothies.

Find the amount for one person before finding the amount for seven.

Twelve rolls are eight rolls plus half of eight rolls.

1. Half of the recipe makes 4 rolls and uses 240\div2=120 ml of milk.
2. For 8+4=12 rolls, use 240+120=360 ml of milk.

Find the amount for one person, then multiply by six.

1. One portion uses 750\div10=75 g of tomatoes.
2. Six portions use 75\times6=450 g.

Work out the price of one notebook first.

1. One notebook costs 8.40\div6=1.40, so its price is £1.40.
2. Five notebooks cost 1.40\times5=7, which is £7.00.

Find how many grams of flour one loaf needs, then divide the available flour by that amount.

1. One loaf uses 640\div8=80 g of flour.
2. The available flour makes 1040\div80=13 loaves.

Work out what multiplies 6 to give 9; the same multiplier must apply to every ingredient.

1. The number of portions is multiplied by 9\div6=1.5.
2. Multiply every ingredient amount by 1.5. Adding 3 does not keep the amount per portion the same, and changing only one ingredient changes the recipe.

Find the amount of each ingredient for one person. For part (b), remember that 1000 ml is 1 litre.

Part (a)

1. Rice for one person: 450\div6=75 g.
2. Rice for ten people: 75\times10=750 g.

Part (b)

1. Stock for one person: 900\div6=150 ml.
2. Stock for ten people: 150\times10=1500 ml.
3. 1500\div1000=1.5, so 1.5 litres of stock are needed.

Find the total flour needed, then choose a whole number of bags that gives at least that much.

1. One roll uses 300\div4=75 g of flour.
2. Eighteen rolls need 75\times18=1350 g.
3. Two bags contain 2\times500=1000 g, which is not enough.
4. Three bags contain 3\times500=1500 g, so the smallest number is 3 bags.

Convert the juice to millilitres and find the number of lollies before calculating the money received.

1. 1.8 litres is 1800 ml.
2. 1800\div600=3, so there is enough juice for three recipes.
3. This makes 3\times8=24 lollies.
4. The money received is 24\times65=1560 pence, which is £15.60.

Find the butter needed for a bag of four biscuits, then find how many such bags the available butter will make.

1. Four biscuits are one third of 12, so they use 90\div3=30 g of butter.
2. Each full bag therefore needs 30 g of butter.
3. 240\div30=8, so the baker can fill 8 bags.

First work out how much nine portions should use; then compare this with the amount Finn has measured.

1. One portion uses 450\div6=75 g.
2. Nine portions need 75\times9=675 g.
3. Finn must add 675-600=75 g of rice.

Put the available amounts into grams and millilitres, then compare every ingredient with the amount needed for sixteen loaves.

Part (a)

1. Flour needed: 500\div10\times16=800 g.
2. Zara has 0.9\times1000=900 g, so she needs 0 g more.

Part (b)

1. Milk needed: 300\div10\times16=480 ml.
2. Zara has 0.45\times1000=450 ml, so she needs 480-450=30 ml more.

Part (c)

1. Oil needed: 50\div10\times16=80 ml.
2. Zara has 0.1\times1000=100 ml, so she needs 0 ml more.

Work out the number each ingredient could make on its own. The ingredient that runs out first limits the answer.

1. One flapjack needs 200\div8=25 g of oats and 80\div8=10 g of butter.
2. The oats could make 900\div25=36 flapjacks. The butter could make 300\div10=30 flapjacks.
3. The sugar could make 240\div60=4 recipes, which is 4\times8=32 flapjacks.
4. The smallest of these numbers is 30. Butter runs out first, so the greatest number is 30 whole flapjacks.
5. Check the other ingredients for 30: oats =25\times30=750 g and sugar =60\div8\times30=225 g. Both are within the amounts available.

Scale both ingredient amounts to twenty-seven portions. Round each number of containers up before calculating the total cost.

1. One portion needs 350\div5=70 g of lentils. For 27 portions, 70\times27=1890 g are needed.
2. Three bags contain 1500 g, which is too little; four contain 2000 g. The group needs 4 bags.
3. One portion needs 600\div5=120 g of tomatoes. For 27 portions, 120\times27=3240 g are needed.
4. Eight tins contain 8\times400=3200 g, which is 40 g too little. The group needs 9 tins.
5. Four bags cost 4\times1.60=6.40, or £6.40.
6. Nine tins cost 9\times0.85=7.65, or £7.65.
7. Total cost: 6.40+7.65=14.05, or £14.05.

Compare 360 ml of milk with the 120 ml in the recipe to see how many times the recipe she is making. Then find the flour and sugar she needs and subtract what is already in the bowl.

Part (a)

1. 360\div120=3, so Amira is making the recipe 3 times (24 muffins).
2. Flour needed: 240\times3=720 g.
3. She must add 720-600=120 g of flour.

Part (b)

1. 360\div120=3, so every ingredient is multiplied by 3.
2. Sugar needed: 160\times3=480 g.
3. She must add 480-400=80 g of sugar.

Find the ingredients needed for one bag of six buns. Check both ingredients before deciding the number of bags.

Part (a)

1. One bag of 6 buns needs 450\div2=225 g of flour and 180\div2=90 g of butter.
2. There are 2000 g of flour. Eight bags use 8\times225=1800 g, but nine need 2025 g. Flour allows only 8 full bags.
3. Eight bags use 8\times90=720 g of butter, but nine need 810 g. Butter also allows only 8 full bags.
4. The greatest number is 8 complete bags.

Part (b)

1. Eight bags use 8\times225=1800 g of flour.
2. Flour remaining: 2000-1800=200 g.

Part (c)

1. Eight bags use 8\times90=720 g of butter.
2. Butter remaining: 750-720=30 g.