Chapter 1 Use Positive Rational Numbers
Section 1.2 Fluently Divide Whole Numbers And Decimals
Page 13 Exercise 1 Answer
Some friends went to lunch and split the bill equally. The bill was $27. since each person paid $6.75, four people went to lunch.
Suppose $7.00 was added to the bill for a dessert that everyone shared. How much more does each person have to pay?
One way to find the answer is to add $7.00 to $27 and then divide by 4. The the answer is the difference between the result and $6.75.
Another way to find the answer is to simply divide $7 by four. Then the result the answer.
Result
Each person has to pay $1.75 more.
Read And Learn More: enVisionmath 2.0 Grade 6 Volume 1 Solutions
Page 13 Exercise 1 Answer
We know that the total bill was $27 and that each person paid $6.75. We need to find how many people went to lunch.
To solver this equation, we can use a diagram or an equation. I have chosen to use a diagram.
To use a diagram, start by drawing boxes and label each one with 6.75. We need to find how many of these boxes give a total of $27:
We needed 4 boxes to get a total of 27 so 4 people went to lunch.
Result
4 people
Page 14 Exercise 1 Answer
Workers at an electronics company pack 2.610 smart phones in boxes. Each box holders 9 smart phones. How many boxes do they fill?
Result
They fill 290 boxes.
Page 15 Exercise 2a Answer
Dividing 65 and 8 gives:
There is a remainder of 1 so to continue dividing, we need to place a decimal point in the divisor and quotient. Then write additional 0s to the right of the decimal point until we no longer have a remainder:
Therefore 65 ÷ 8 = 8.125
Result
8.125
Page 15 Exercise 2b Answer
Use long division method to divide the numbers.
Result
1.8
Page 15 Exercise 2c Answer
We need to find 128.8 ÷ 1.4.
Since the divisor of 1.4 is not a whole number, we first need to multiply the dividend and divisor by the same power of 10 to get a whole number divisor.
Since 1.4 has 1 decimal place, we can multiply by 101, or 10:
128.8 ÷ 1.4 = 1288 ÷ 14
Dividing 1288 and 14 gives:
Therefore, 128.8 ÷ 1.4 = 92
Result
92
Page 16 Exercise 1 Answer
When dividing by a decimal, rewrite the decimal so that you are dividing by a whole number.
For example,
22.78 ÷ 3.4
Multiply both the divisor and the divident by the same power of 10.
22.78 x 10 = 22.78
3.4 x 10 = 34
Then divide as you would with a whole number.
Result
When divided by a decimal, rewrite the decimal so that you are dividing by a whole number. Then divide as you would with a whole number.
Page 16 Exercise 2 Answer
When dividing, the divisor must always be a whole number. When dividing with the decimals, it is then necessary to multiply the divisor and divident by the same power of 10 so the divisor will become a whole number.
For example, if we wanted to find 121 ÷ 0.11, we would multiply the divisor and dividend by 102 = 100 since this would give a whole number divisor of 0.11 x 100 = 11
Result
It is necessary because we need to divide using a whole number divisor.
Page 16 Exercise 3 Answer
When dividing 6,139 by 153 we will start by dividing 613 by 153, thus the first digit of the quotient is placed above the digit 3 in 6,139.
Result
We start by dividing 613 by 153 so the first digit of the quotient is placed above the digit 3 in 6,139.
Page 16 Exercise 4 Answer
When dividing a decimal by a whole number, divide the numbers ignoring the decimal point, than put the decimal point in the answer the decimal point in the dividend.
Result
Put the decimal point in the answer directly above the decimal point in the dividend.
Page 16 Exercise 5 Answer
Use long division method to divide the numbers.
Result
The result is 205 and the remainder is 13.
Page 16 Exercise 6 Answer
Use long division method to divide the numbers.
Result
The quotient is 77 and the remainder is 17.
Page 16 Exercise 7 Answer
Use long division method to divide the numbers.
Result
The quotient is 8 and the remainder is 9.
Page 16 Exercise 8 Answer
Use long division method to divide the numbers.
Result
The result is 34.75
Page 16 Exercise 9 Answer
Use long division method to divide the numbers.
Result
The result is 107.5
Page 16 Exercise 10 Answer
Use long division method to divide the numbers.
Result
6.95
Page 16 Exercise 11 Answer
Use long division method to divide the numbers.
Result
43.05
Page 16 Exercise 12 Answer
We need to find the quotient 5.3 ÷ 0.2.
To divide decimals, the divisor must be a whole number so you will first need to multiply the numerator and denominator by the same power of 10.
Since the divisor 0.2 has one decimal point, multiply both numbers by 101 = 10 to get 5.3 ÷ 0.2 = 5.3 ÷ 2.
To complete the division, write a decimal point in the dividend, a decimal point in the quotient directly above the one in the dividend, and then annex a zero to the right of the decimal point in the dividend:
Therefore, 5.3 ÷ 0.2 = 26.5
Result
26.5
Page 16 Exercise 13 Answer
We need to find the quotient 8.9 ÷ 0.4.
To divide decimals, the divisor must be a whole number so you will first need to multiply the numerator and denominator by the same power of 10.
Since the divisor 0.4 has one decimal point, multiply both numbers by 101 = 10 to get 8.9 ÷ 0.4 = 89 ÷ 4.
To complete the divison, write a decimal point in the dividend, a decimal point in the quotient directly above the one in the dividend, and then annex zeros to the right of the decimal point in the dividend:
Therefore, 8.9 ÷ 0.4 = 22.25
Result
22.25
Page 17 Exercise 14 Answer
Use long division method to divide the numbers.
Result
94
Page 17 Exercise 15 Answer
4 does not divide into 350 evenly so we need to annex a 0 to the right of the decimal point in the dividend. Dividing then gives:
Result
87.5
Page 17 Exercise 16 Answer
Use long division method to divide the numbers.
Result
123
Page 17 Exercise 17 Answer
Use long division method to divide the numbers.
Result
364
Page 17 Exercise 18 Answer
Use long division method to divide the numbers.
Result
275
Page 17 Exercise 19 Answer
Use long division method to divide the numbers.
Result
25
Page 17 Exercise 20 Answer
Use long division method to divide the numbers.
Result
11.2
Page 17 Exercise 21 Answer
Use long division method to divide the numbers.
Result
5.8
Page 17 Exercise 22 Answer
Use long division method to divide the numbers.
Result
4.4
Page 17 Exercise 23 Answer
Use long division method to divide the numbers.
Result
656.6
Page 17 Exercise 24 Answer
Use long division method to divide the numbers.
Result
9.03
Page 17 Exercise 25 Answer
Use long division method to divide the numbers.
Result
23.4
Page 17 Exercise 26 Answer
Use long division method to divide the numbers.
Result
0.9
Page 17 Exercise 27 Answer
Use long division method to divide the numbers.
Result
27.5
Page 17 Exercise 28 Answer
To find 6.4 ÷ 0.8, we first need to multiply the divisor and dividend by the same power of 10 to get a whole number divisor.
Multiplying by 10 gives 6.4 ÷ 0.8 = 64 ÷ 8.
Since 64 ÷ 8 = 8, then 6.4 ÷ 0.8 = 8
Result
8
Page 17 Exercise 29 Answer
To find 0.2430 ÷ 0.6, we first need to multiply the divisor and dividend by the same power of 10 to get a whole number divisor.
Multiplying by 10 gives 0.2430 ÷ 0.6 = 2.430 ÷ 6.
To divide 2.430 and 6, start by writing the decimal point in the quotient directly above the decimal point in the dividend. Then divide as you would with whole numbers:
Therefore, 0.2430 ÷ 0.6 = 0.405
Result
0.405
Page 17 Exercise 30 Answer
To find 52.056 ÷ 7.23, we first need to multiply the divisor and dividend by the same power of 10 to get a whole number divisor.
Multiplying by 100 gives 52.056 ÷ 7.23 = 5205.6 ÷ 723.
To divide 5205.6 and 723, start by writing the decimal point in the quotient directly above the decimal point in the dividend. Then divide as you would with whole numbers:
Therefore, 52.056 ÷ 7.23 = 7.2
Result
7.2
Page 17 Exercise 31 Answer
To find 9.089 ÷ 0.745, we first need to multiply the divisor and dividend by the same power of 10 to get a whole number divisor.
Multiplying by 1000 gives 9.089 ÷ 0.745 = 9089 ÷ 745.
745 doesn’t divide evenly into 9089 so write a decimal point in the dividend, a decimal point in the quotient directly above the decimal point in the dividend, and annex a 0 so you can complete the division:
Therefore, 9.089 ÷ 0.745 = 12.2
Result
12.2
Page 17 Exercise 32 Answer
The Thorny Devil lizard can eat 45 ants per minute and we need to find out how long it would take this lizard to eat 1,080 ants. To find the time, we need to divide 1,080 by 45.
Use long division method to divide the numbers.
The lizard takes 24 minutes to eat 1,080 ants.
Result
It would take lizard 24 minutes to eat 1,080 ants.
Page 18 Exercise 33 Answer
Henrieta’s response is not correct because she made a mistake. She forgot to write down a zero when she divided 8 by 20, and instead, she wrote down 4 when she divided 80 by 20. The correct response is 0.04 as seen below.
Result
She forgot to write down a zero when she divided 8 by 20. The correct response is 0.04.
Page 18 Exercise 34 Answer
Between two brands of fruit snacks, Brand A and Brand B, which of them costs less per pound and how much?
15lb of Brand A cost $16.20 and 25 lb of Brand B cost $22.25. To calculate how much each of them costs per pount we need to divide 16.2 by 15 and 22.25 by 25.
Brand A costs $1.08 per pound and Brand B $0.89 per pound.
Brand B costs $0.19 less per pound.
Result
Brand A costs $ 1.08 per pound and Brand B $0.89 per poind, so Brand B costs $0.19 less per pound.
Page 18 Exercise 35 Answer
Movie tickets in 1960 cost $ 0.75 and in 2010 they cost $ 9.75. Regular Popcorn in 1960 cost $0.25 and in 2010 it cost $4.10. Regular Drink in 1960 cost $0.35 and in 2010 it cost $3.08.
To find how many times as much each item costs in 2010 as ain 1960, we need to calculate the following:
The numbers 9.75, 4.10 and 3.08 can be written as:
9.75 = 0.75 x 13,
4.10 = 0.25 x 16.4,
3.08 = 0.35 x 8.8.
Thus, movie tickets in 2010 cost 13 times as much as in 1960, regular popcorn in 2010 cost 16.4 times as much as in 1960, and regular drink in 2010 cost 8.8 times as much as in 1960.
Result
Movie tickets in 2010 cost 13 times as much as in 1960, regular popcorn 16.4 times as much and regular dringk 8.8 times as much.
Page 18 Exercise 36 Answer
Kendra has to find out how many pounds of popcorn she needs to put in each of the 50 bags so that the 5.5 pounds of popcorn she has will be equally distributed. She must divide 5.5 by 50.
Result
Kendra has to put 0.11 pound of popcorn in each bag.
Page 18 Exercise 37 Answer
You and your friend got paid $38.25 for 2.5 + 2 = 4.5 hours of work, which means we can divide $ 38.25 by 4.5 and then multiply that by 2.5 to find how much money you earned.
Your share of the money is $21.25.
Result
Your share of the money is $21.25.
Page 18 Exercise 38 Answer
Use long division method to divide the numbers.
So, the pairs are:
21.6 ÷ 3 = 7.2,
315.7 ÷ 41 = 7.7,
90 ÷ 12 = 7.5.
Result
21.6 ÷ 3 = 7.2,
315.7 ÷ 41 = 7.7,
90 ÷ 12 = 7.5.
Page 18 Exercise 39 Answer
Use long division method to divide the numbers.
So, the pairs are:
632.5 ÷ 4.5 = 141,
1,354 ÷ 44 = 31,
1,248 ÷ 0.25 – 4,992.
Result
632.5 ÷ 4.5 = 141,
1,354 ÷ 44 = 31,
1,248 ÷ 0.25 – 4,992.