Estimating products by rounding
Estimate first and use that to check the result. 8 × 67 = ?
67 can be rounded up
to 70, or 67 ≈ 70.
Therefore 8 × 67 ≈
8 × 70 = 560.
5
67
× 8
356
5
67
× 8
536
Oops! 356 is
far from the
estimation 560.
There must be
an error. Can
you find it? This result
sounds right,
because it is
fairly close to
560.
Before we start using estimation as a checking method, let's review the rounding rules.
When rounding to nearest ten,
* If the last digit is __, __, __, or __, round down to the previous ten.
* If the last digit is __, __, __, __, or __, round up to the next ten.
The symbol ≈ is used to indicate rounding, and is read as "is approximately" or "is about".
Examples:
34 ≈ 30
598 ≈ 600
143 ≈ 140
255 ≈ 260
704 ≈ 700
705 ≈ 710
Example problems
1. First estimate the result by rounding the second factor. Then multiply to find out the exact result.
a.
91 ≈ 90
4 × 91 ≈
4 × 90 = 360
91
× 4
364
c.
34 ≈ ____
6 × 34 ≈
6 × ___ = ____
34
× 6
e.
99 ≈ ____
5 × 99 ≈
5 × ___ = ____
99
× 5
g.
48 ≈ ____
3 × 48 ≈
3 × ___ = ____
48
× 3
m.
91 ≈ ____
5 × 91 ≈
5 × ___ = ____
91
× 5
2. These word problems illustrate some situations where you can use estimation.
a) 58 people are invited to the party; you are going to the store to buy supplies. You figure that for each person you need two cups, two plates, and three napkins. How many cups, plates, and napkins do you approximately need?
e) A can of beans costs 29 cents. A bag of lentils costs 42 cents. Estimate which is cheaper: to buy 8 cans of beans or to buy 5 bags of lentils.
h) Jill needs 21 inches of material to make a skirt. About how much should she buy for seven skirts?
Now, add to the answer above 10 inches to make sure she has enough. The material costs 1 dollars per each 9 inches (or 4 dollars a yard). How much will it cost Jill to buy what she needs? Draw a picture! You can for example mark the 9-inch strips in your picture and use that to help.
i) What if you have a situation similar to the one in a) but just with 92 people. How many cups, plates, and napkins would you need?
How many packages of each would you buy?
Estimate first and use that to check the result. 8 × 67 = ?
67 can be rounded up
to 70, or 67 ≈ 70.
Therefore 8 × 67 ≈
8 × 70 = 560.
5
67
× 8
356
5
67
× 8
536
Oops! 356 is
far from the
estimation 560.
There must be
an error. Can
you find it? This result
sounds right,
because it is
fairly close to
560.
Before we start using estimation as a checking method, let's review the rounding rules.
When rounding to nearest ten,
* If the last digit is __, __, __, or __, round down to the previous ten.
* If the last digit is __, __, __, __, or __, round up to the next ten.
The symbol ≈ is used to indicate rounding, and is read as "is approximately" or "is about".
Examples:
34 ≈ 30
598 ≈ 600
143 ≈ 140
255 ≈ 260
704 ≈ 700
705 ≈ 710
Example problems
1. First estimate the result by rounding the second factor. Then multiply to find out the exact result.
a.
91 ≈ 90
4 × 91 ≈
4 × 90 = 360
91
× 4
364
c.
34 ≈ ____
6 × 34 ≈
6 × ___ = ____
34
× 6
e.
99 ≈ ____
5 × 99 ≈
5 × ___ = ____
99
× 5
g.
48 ≈ ____
3 × 48 ≈
3 × ___ = ____
48
× 3
m.
91 ≈ ____
5 × 91 ≈
5 × ___ = ____
91
× 5
2. These word problems illustrate some situations where you can use estimation.
a) 58 people are invited to the party; you are going to the store to buy supplies. You figure that for each person you need two cups, two plates, and three napkins. How many cups, plates, and napkins do you approximately need?
e) A can of beans costs 29 cents. A bag of lentils costs 42 cents. Estimate which is cheaper: to buy 8 cans of beans or to buy 5 bags of lentils.
h) Jill needs 21 inches of material to make a skirt. About how much should she buy for seven skirts?
Now, add to the answer above 10 inches to make sure she has enough. The material costs 1 dollars per each 9 inches (or 4 dollars a yard). How much will it cost Jill to buy what she needs? Draw a picture! You can for example mark the 9-inch strips in your picture and use that to help.
i) What if you have a situation similar to the one in a) but just with 92 people. How many cups, plates, and napkins would you need?
How many packages of each would you buy?
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