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Question 1 of 4
Add the following:
978+3524
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A mixed number consists of a whole number and a fraction.
First, add the whole numbers
Notice that the fractions have different denominators.
Find the LCD of 8 and 24 so we can add the fractions.
The LCD of 8 and 24 is 24
Proceed with adding the fractions
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78+524 |
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= |
7×38×3+524 |
Multiply by 3 so that the denominator becomes 24 |
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= |
2124+524 |
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= |
2624 |
Change the improper fraction to a mixed fraction
Divide the numerator by the denominator
Arrange the numbers for long division
24 goes into 26 one time. So write 1 above the line.
Multiply 1 to 24 and write the answer below 26
Subtract 24 from 26 and write the answer one line below
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Since 24 cannot go into 2 anymore, 2 is left as the Remainder and 1 is the Quotient
Substitute values into the given formula
bc |
= |
QRc |
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2624 |
= |
1224 |
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= |
12÷224÷2 |
Express in lowest terms |
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= |
1112 |
Finally, combine the sum of the whole numbers and the sum of the fractions
978+3524 |
= |
12+1112 |
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= |
13112 |
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Question 2 of 4
Subtract the following:
7-338
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First, transform the mixed fractions to improper fractions
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7−338 |
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= |
71−(8×3)+38 |
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= |
71−24+38 |
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= |
71−278 |
Use cross method to subtract the fractions.
Start by multiplying the two denominators. Use the product as a denominator for a new fraction.
To get the numerator, cross multiply the given addition problem and subtract the products.
71−278 |
= |
(7×8)−(1×27)8 |
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= |
56-278 |
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= |
298 |
Transform the fraction back to a mixed fraction
Start by dividing the numerator by the denominator
Arrange the numbers for long division
8 goes into 29 six times. So write 6 above the line.
Multiply 3 to 8 and write the answer below 29
Subtract 24 from 29 and write the answer one line below
Since 8 cannot go into 5 anymore, 5 is left as the Remainder and 3 is the Quotient
Substitute values into the given formula
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Question 3 of 4
Subtract the following:
514-323
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First, transform the mixed fractions to improper fractions
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514−323 |
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= |
(4×5)+14−(3×3)+23 |
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= |
20+14−9+23 |
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= |
214−113 |
Notice that the fractions have different denominators.
Find the LCD of 4 and 3 so we can subtract the fractions.
Multiples of 3:
369121518
Next, we get the same denominator and subtract the fractions
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214-113 |
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= |
21×34×3−11×43×4 |
Multiply each fraction so that the denominator becomes 12 |
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= |
6312−4412 |
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= |
1912 |
Transform the fraction back to a mixed fraction
Start by dividing the numerator by the denominator
Arrange the numbers for long division
12 goes into 19 once. So write 1 above the line.
Multiply 1 to 12 and write the answer below 19
Subtract 12 from 19 and write the answer one line below
Since 12 cannot go into 7 anymore, 7 is left as the Remainder and 1 is the Quotient
Substitute values into the given formula
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Question 4 of 4
Subtract the following:
9-2710
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First, transform the mixed fractions to improper fractions
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9−2710 |
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= |
91−(10×2)+710 |
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= |
91−20+710 |
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= |
91−2710 |
Use cross method to subtract the fractions.
Start by multiplying the two denominators. Use the product as a denominator for a new fraction.
To get the numerator, cross multiply the given addition problem and subtract the products.
91−2710 |
= |
(9×10)−(1×27)10 |
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= |
90-2710 |
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= |
6310 |
Transform the fraction back to a mixed fraction
Start by dividing the numerator by the denominator
Arrange the numbers for long division
10 goes into 63 six times. So write 6 above the line.
Multiply 6 to 10 and write the answer below 63
Subtract 60 from 63 and write the answer one line below
Since 10 cannot go into 3 anymore, 3 is left as the Remainder and 6 is the Quotient
Substitute values into the given formula