5A Core skills 1. Which amount in each of the following pairs is smaller? Justify your answer. (i) 40% or 1
__ 4
(ii) 0·4 or 5
__ 8
(iii) 0·5 or 5%
2. Write the following amounts in descending (largest to smallest) order. 12% 3
__ 8 0·0123 42% 1
__ 5 0·45
3. Write the following amounts in ascending order, i.e. smallest to largest. Where necessary, round to two decimal places.
30% 1
__ 3 , 0·35
(iii) 69 out of 320 (iv) 38 out of 72
__ 7 45% 0·04
3
4. Change each of the following into percentages. Give your answers to three signifi cant fi gures. (i) 43 out of 250 (ii) 37 out of 40
(v) 45 out of 120 (vi) 78 out of 356
5. Which amount in each of the following pairs is bigger? (i) 75% of 65 or 70% of 93
6. Find the value of each of the following. (i) 1
_ 2 × 3
_ 5 + 1
_ 4
(ii) 5
_ 6 − 1
_ 5 × 5
_ 8 + 2
_ 3
How many black beads are on the long necklace?
8. Copy the table below and put a tick (✓) in the correct box in each row to show whether each statement is always true, sometimes true, or never true.
Statement (i)
Three is less than four, so one-third of a chocolate bar must be smaller than one-quarter of the same chocolate bar.
(ii) 2
__ 3 + 3
__ 5 = 5
__ 8
(iii) A natural number can be written as a fraction.
(iv) 3% is the same as 0·3 (v) Percentages are between 0% and 100%. (vi) 1
__ 2 of 1
__ 3 is 1
__ 6
(vii) Half of a Hawaiian pizza is the same as half of a pepperoni pizza.
Tick one box only for each statement Always true Sometimes true Never true (ii) 85% of 17 or 10% of 649
(iii) (1 _
4 + 5 _
6 − 1 _
(iii) 65% of 180 or 34% of 712
3 ) × 8 _
5 (iv) 14
7. A short necklace has 32 gold beads and 8 black beads. A long necklace has a total of 60 beads. Both necklaces have the same fraction of gold beads and black beads.