Year 6 Maths reasoning (SATs): Sharing in a ratio and fractions of a total

Method. Find the total parts, then the value of one part.

1. Find the total number of parts. 1 + 2 = 3 parts.
   3 parts
2. Find the value of one part. 90 / 3 = 30.
   1 part = 30
3. Multiply each ratio number by one part. Tom: 1 x 30 and Sam: 2 x 30
   30, 60
4. Write the answer.
   30, 60

Check. 30 + 60 = 90. ✓

Watch out. Check that the amounts add up to the total.

Method. Find the total parts, then the value of one part.

1. Find the total number of parts. 3 + 5 = 8 parts.
   8 parts
2. Find the value of one part. 144 / 8 = 18.
   1 part = 18
3. Multiply each ratio number by one part. Mia: 3 x 18 and Leo: 5 x 18
   54, 90
4. Write the answer.
   54, 90

Check. 54 + 90 = 144. ✓

Watch out. Check that the amounts add up to the total.

Method. Find the total parts, then the value of one part.

1. Find the total number of parts. 2 + 3 + 5 = 10 parts.
   10 parts
2. Find the value of one part. 500 / 10 = 50.
   1 part = 50
3. Multiply each ratio number by one part. Ava: 2 x 50 and Ben: 3 x 50 and Cy: 5 x 50
   100, 150, 250
4. Write the answer.
   100, 150, 250

Check. 100 + 150 + 250 = 500. ✓

Watch out. Check that the amounts add up to the total.

Method. The total is the sum of all the parts, so the fraction is that part over the total.

1. Find the total number of parts. 3 + 4 = 7.
   7 parts
2. Write the part as a fraction of the total, in simplest form. The part is 4 out of 7 parts, which simplifies to 4/7.
   4/7
3. Write the answer.
   4/7

Check. 4 + 3 = 7. ✓

Watch out. The fraction uses the total of all parts, not the other part only.

Method. The total is the sum of all the parts, so the fraction is that part over the total.

1. Find the total number of parts. 1 + 3 = 4.
   4 parts
2. Write the part as a fraction of the total, in simplest form. The part is 1 out of 4 parts, which simplifies to 1/4.
   1/4
3. Write the answer.
   1/4

Check. 1 + 3 = 4. ✓

Watch out. The fraction uses the total of all parts, not the other part only.

Method. The total is the sum of all the parts, so the fraction is that part over the total.

1. Find the total number of parts. 2 + 5 + 3 = 10.
   10 parts
2. Write the part as a fraction of the total, in simplest form. The part is 3 out of 10 parts, which simplifies to 3/10.
   3/10
3. Write the answer.
   3/10

Check. 3 + 7 = 10. ✓

Watch out. The fraction uses the total of all parts, not the other part only.

Method. The total is the sum of all the parts, so the fraction is that part over the total.

1. Find the total number of parts. 2 + 4 = 6.
   6 parts
2. Write the part as a fraction of the total, in simplest form. The part is 2 out of 6 parts, which simplifies to 1/3.
   1/3
3. Write the answer.
   1/3

Check. 2 + 4 = 6. ✓

Watch out. The fraction uses the total of all parts, not the other part only.

Method. Find the value of one part, then the difference in parts.

1. Total parts. 2 + 3 = 5 parts.
   5 parts
2. One part. 75 / 5 = 15 pounds.
   15 pounds
3. Difference. Jo has 3 parts and Priya has 2 parts, so the difference is 1 part, which is 15 pounds.
   15 pounds
4. Write the answer.
   15

Check. Priya 30 and Jo 45: 45 - 30 = 15. ✓

Method. Divide both parts of the ratio by the highest common factor.

1. Find the highest common factor of both numbers. The biggest number that divides 12 and 18 is 6.
   HCF = 6
2. Divide both parts by it. 12 / 6 = 2 and 18 / 6 = 3.
   2:3
3. Write the answer.
   2:3

Check. 2 and 3 have no common factor except 1. ✓

Watch out. Both parts must be divided by the same number, just as with a fraction.

Method. Test each choice against the question.

1. Read what the question asks. Decide what the answer must do or show.
2. Test the choice. The total is 2 + 3 = 5 parts, so the first part is 2/5.
   No, it is 2/5 of the total fits
3. Reject the other choices. 2/3 compares the first part with the second, not with the total.
   Yes, it is 2/3 of the total and No, it is 2/3 of the second part only do not fit
4. Write the answer.
   No, it is 2/5 of the total

Check. No, it is 2/5 of the total is the one that fits. ✓

Method. Find the value of one part.

1. Total parts. 2 + 1 = 3 parts.
   3 parts
2. One part. 30 / 3 = 10.
   10
3. Sopranos. 2 parts: 2 x 10 = 20.
   20
4. Write the answer.
   20

Check. 20 sopranos and 10 altos make 30. ✓

Method. Think about the parts.

1. Look at the parts. The first amount has 1 part and the second has 2 parts.
   1 and 2
2. Compare. 2 parts is twice 1 part.
   twice as big
3. Write the answer.
   Because for each one part of the first amount there are two parts of the second, so the second is twice as big.

Check. 2 = 2 x 1. ✓

Method. Find the value of one part from Tom's share.

1. One part. 24 / 4 = 6 sweets.
   6
2. Total. There are 4 + 5 = 9 parts, so 9 x 6 = 54.
   54
3. Write the answer.
   54

Check. 24 + 30 = 54. ✓

Method. Find the value of one part from the largest share.

1. One part. 36 / 3 = 12 pounds.
   12
2. Total parts. 1 + 2 + 3 = 6 parts, so 6 x 12 = 72.
   72
3. Write the answer.
   72

Check. 12 + 24 + 36 = 72. ✓

Method. Find the total number of parts, then write the middle part as a fraction.

1. Total parts. 1 + 2 + 3 = 6 parts.
   6 parts
2. Middle part. The middle person has 2 parts, so 2/6.
   2/6
3. Simplify. The HCF of 2 and 6 is 2, so 2/6 = 1/3.
   1/3
4. Write the answer.
   1/3

Check. 2/6 = 1/3. ✓