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Question 1 of 3
Add the following:
812+1034
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A mixed number consists of a whole number and a fraction.
Method One
First, add the whole numbers
Notice that the fractions have different denominators.
Find the LCD of 2 and 4 so we can add the fractions.
Use the LCD as the denominator for both fractions then proceed with adding.
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12+34 |
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= |
1×22×2+34 |
Multiply by 2 so that the denominator becomes 4 |
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= |
24+34 |
Add the numerators |
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= |
54 |
Keep the same denominator |
Change the improper fraction to a mixed fraction
Divide the numerator by the denominator
Arrange the numbers for long division
4 goes into 5 one time. So write 1 above the line.
Multiply 1 to 4 and write the answer below 5
Subtract 4 from 5 and write the answer one line below
Since 4 cannot go into 1 anymore, 1 is left as the Remainder and 1 is the Quotient
Substitute values into the given formula
Finally, combine the sum of the whole numbers and the sum of the fractions
Method Two
First, add the whole numbers
Add the fractions using cross method.
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 add the products.
12+34 |
= |
(1×4)+(2×3)8 |
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= |
4+68 |
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= |
108 |
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= |
10÷28÷2 |
Express in lowest terms |
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= |
54 |
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= |
114 |
We know this from Method One |
Finally, combine the sum of the whole numbers and the sum of the fractions
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Question 2 of 3
Add the following:
723+357
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A mixed number consists of a whole number and a fraction.
First, add the whole numbers
Add the fractions using cross method.
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 add the products.
23+57 |
= |
(2×7)+(3×5)21 |
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= |
14+1521 |
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= |
2921 |
Change the improper fraction to a mixed fraction
Divide the numerator by the denominator
Arrange the numbers for long division
21 goes into 29 one time. So write 1 above the line.
Multiply 1 to 21 and write the answer below 29
Subtract 21 from 29 and write the answer one line below
Since 21 cannot go into 8 anymore, 8 is left as the Remainder and 1 is the Quotient
Substitute values into the given formula
bc |
= |
QRc |
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2921 |
= |
1821 |
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= |
1821 |
Finally, combine the sum of the whole numbers and the sum of the fractions
723+357 |
= |
10+1821 |
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= |
11821 |
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Question 3 of 3
Subtract the following:
412-2110
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First, transform the mixed fractions to improper fractions
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412−2110 |
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= |
(2×4)+12−(10×2)+110 |
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= |
8+12−20+110 |
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= |
92−2110 |
Notice that the fractions have different denominators.
Find the LCD of 2 and 10 so we can subtract the fractions.
The LCD of 2 and 10 is 10
Next, we get the same denominator and subtract the fractions
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92-2110 |
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= |
9×52×5−2110 |
Multiply 5 so that the denominator becomes 10 |
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= |
4510−2110 |
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= |
2410 |
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 24 two times. So write 2 above the line.
Multiply 2 to 10 and write the answer below 24
Subtract 20 from 24 and write the answer one line below
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Since 10 cannot go into 4 anymore, 4 is left as the Remainder and 2 is the Quotient
Substitute values into the given formula
bc |
= |
QRc |
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2410 |
= |
2410 |
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= |
24÷210÷2 |
Reduce to lowest terms |
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= |
225 |