Writing and Simplifying Ratios

Keep the colour order and divide both counts by the same common factor.

Find the largest number that divides both terms.

Divide both numbers by their largest common factor.

Reversing the order of the categories reverses the order of the numbers.

Find what multiplies 4 to give 20 and apply it to 7.

Divide both terms by their highest common factor.

Part (a)

1. Divide both terms by 6: 18:24=3:4.
2. So a=3.

Part (b)

1. Divide both terms by 6: 18:24=3:4.
2. So b=4.

Use the same divisor for all three numbers.

Part (a)

1. All three numbers divide by 5: 15:25:35=3:5:7.
2. There is no common factor above 1 for all three remaining terms.
3. So a=3.

Part (b)

1. All three numbers divide by 5: 15:25:35=3:5:7.
2. There is no common factor above 1 for all three remaining terms.
3. So b=5.

Part (c)

1. All three numbers divide by 5: 15:25:35=3:5:7.
2. There is no common factor above 1 for all three remaining terms.
3. So c=7.

Put both lengths into centimetres before comparing them.

1. 1.2 m is 120 cm, so the ratio is 30:120.
2. Divide both terms by 30 to get 1:4. Therefore n=4.

Count the total parts before writing the fraction.

1. There are 3+8=11 equal parts altogether.
2. Red counters make up 3 of them, so the fraction is \frac3{11}.

The second ratio term represents dogs, not all the animals.

Part (a)

1. Cats account for 2 out of every 7 animals. Dogs account for 7-2=5.
2. The ratio cats : dogs is 2:5.
3. So a=2.

Part (b)

1. Cats account for 2 out of every 7 animals. Dogs account for 7-2=5.
2. The ratio cats : dogs is 2:5.
3. So b=5.

Multiply both terms by 10 first, then simplify the resulting whole numbers.

Part (a)

1. Multiply both terms by 10: 0.8:1.2=8:12.
2. Divide both by 4 to get 2:3, so a=2.

Part (b)

1. After multiplying by 10 and dividing by 4, the second term is 12\div4=3.
2. So b=3 and the complete ratio is 2:3.

Convert kilograms to grams before looking for a common factor.

Part (a)

1. 2.5 kg is 2500 g, so the ratio is 2500:750.
2. Divide both terms by 250 to get 10:3. Therefore a=10.

Part (b)

1. The second term is 750\div250=3.
2. The simplified ratio is 10:3, so b=3.

Match 35 to the five red parts, then find two parts.

1. Five parts contain 35 beads, so one part contains 35\div5=7 beads.
2. Blue beads take two parts: 2\times7=14.

Divide both terms by the first term so that the first becomes 1.

1. Divide both terms by 6. The first is 6\div6=1.
2. The second is 21\div6=3.5. The ratio is 1:3.5, so n=3.5.

Divide both terms by the second term so that the second becomes 1.

1. Divide both terms by 18. The second is 18\div18=1.
2. The first is 45\div18=2.5. The ratio is 2.5:1, so n=2.5.

Find the ratio of vegetarian to non-vegetarian meals before using the given count.

1. Vegetarian meals take 3 of 8 parts, so non-vegetarian meals take 8-3=5 parts.
2. The 45 non-vegetarian meals represent 5 parts. One part is 45\div5=9 meals.
3. Vegetarian meals: 3\times9=27.

Compare the remaining lengths using the same units, then simplify.

Part (a)

1. The first ribbon starts at 1.25\times1000=1250 mm.
2. Its remaining length is 1250-250=1000 mm.
3. The required ratio is 1000:875=8:7, dividing both numbers by 125.
4. So a=8.

Part (b)

1. The first ribbon starts at 1.25\times1000=1250 mm.
2. Its remaining length is 1250-250=1000 mm.
3. The required ratio is 1000:875=8:7, dividing both numbers by 125.
4. So b=7.

Find the original numbers of both colours, then change the green count before simplifying.

Part (a)

1. Blue counters: 0.35\times200=70. Green counters originally: 200-70=130.
2. After removal, there are 130-25=105 green counters and still 70 blue counters.
3. The new ratio is 70:105. Dividing both terms by 35 gives 2:3.
4. So a=2.

Part (b)

1. Blue counters: 0.35\times200=70. Green counters originally: 200-70=130.
2. After removal, there are 130-25=105 green counters and still 70 blue counters.
3. The new ratio is 70:105. Dividing both terms by 35 gives 2:3.
4. So b=3.

The known volume is the concentrate share, not the total. Find the volume of one ratio part.

1. Two ratio parts are 0.6 litres, so one part is 0.6\div2=0.3 litres.
2. The whole drink has 2+9=11 parts.
3. Total volume: 11\times0.3=3.3 litres.

Find the original blue count, change only the red count, then simplify the new ratio.

Part (a)

1. One part originally contains 30\div5=6 counters, so there are 8\times6=48 blue counters.
2. After the addition there are 30+12=42 red counters and still 48 blue counters.
3. The new ratio is 42:48=7:8, after dividing both terms by 6.
4. So a=7.

Part (b)

1. One part originally contains 30\div5=6 counters, so there are 8\times6=48 blue counters.
2. After the addition there are 30+12=42 red counters and still 48 blue counters.
3. The new ratio is 42:48=7:8, after dividing both terms by 6.
4. So b=8.