time yourselfMaths A (practice)Tue 13 October1 / 4
Averages and decimal multiplication: practice
Last week's three ideas, once more with your own hands. Estimate before and after calculating
Name Date
Last week, in three lines1. Average = add everything, divide by how many (it levels out the bumps). Run it backwards: average × count = total.
2. Decimal × decimal Multiply as whole numbers, then give the answer as many decimal places as the two factors have together. (0.3 × 0.4: 3 × 4 = 12; ten times and ten times is 100 times, so divide by 100 → 0.12)
3. Estimating a product Multiply by less than 1 and it gets smaller; by more than 1 and it gets bigger.
First, where it goes wrong"Multiplying always makes a number bigger." Only when you multiply by more than 1.
0.5 × 0.8: 5 × 8 = 40, and 1 + 1 = 2 decimal places → 0.40. 0.40 and 0.4 are the same number, so you may drop the last 0 and write 0.4. But 0.04 or 4.0 are different numbers. Estimate first: is the answer smaller than 0.8?
1 · Decimal × decimal: places and estimates
1Calculate 0.5 × 0.8. Also say whether you may drop a 0 at the end of the answer, and why.
Do 5 × 8 first. How many decimal places in all?
22.4 × 0.35
24 × 35 = 840. Ten times and a hundred times makes how many times?
3Find the area of a rectangle 0.6 m by 0.7 m with an area diagram. Divide a 1 m × 1 m square into a 10 × 10 grid, colour in 0.6 m by 0.7 m of it, and count how many 0.01 m² squares that is.
How many squares tall and how many wide is the coloured part?
50.06 × 0.15
Easy to miscount the zeros. After 6 × 15, count 2 + 2 places.
6Answer without calculating. Which of these come out smaller than 12? Choose all of them.
A 12 × 0.9 B 12 × 1.01 C 12 × 0.05 D 12 × 1.5
Look only at whether the multiplier is less or more than 1.
7Working 4.8 × 3.1 in columns gave the digits 1488. Where does the decimal point go? Make an estimate first, then answer.
Seeing 4.8 as about 5 and 3.1 as about 3, about how big is the answer?
2 · Averages (levelling out)
8A child read for 25, 40, 0, 35 and 30 minutes over five days. What is the average per day?
A day with 0 still counts as a day.
9The average of four kanji tests (out of 10) is 6.5. After a fifth test the average should be 7. What must the fifth score be?
Average × count = total. Find the 4-test total and the 5-test total that is needed.
10A child's travel time to school, Monday to Friday, was 12, 14, 13, 15 and 61 minutes (on Friday the train was late).
(1) What is the 5-day average?
(2) What is the average of the 4 days without the 61?
(3) To describe the "usual" journey, which of (1) and (2) fits better? Give a reason.
3 · Putting them together
11An iron bar weighs 0.45 kg per metre. How much does 2.8 m of it weigh? Draw an area diagram or a number line before you write the calculation.
12A car goes 12.5 km on 1 L of petrol. Over three days it used 2.4 L, 3.1 L and 2.3 L.
(1) How many litres a day did it use on average?
(2) How many km a day does that come to on average?
There are two ways for (2): use the average, or use the 3-day total and divide by 3.