Subtract And Write Your Answer As A Mixed Number In Simplest Form. 2 4 9 − 1 2 9 2 \frac{4}{9} - 1 \frac{2}{9} 2 9 4 ​ − 1 9 2 ​

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Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It is written in the form of abca \frac{b}{c}, where aa is the whole number part and bc\frac{b}{c} is the fractional part. In this article, we will learn how to subtract mixed numbers and write the answer in simplest form.

Subtracting Mixed Numbers

To subtract mixed numbers, we need to follow a step-by-step process. The process involves converting the mixed numbers to improper fractions, subtracting the fractions, and then converting the result back to a mixed number.

Step 1: Convert Mixed Numbers to Improper Fractions

To convert a mixed number to an improper fraction, we need to multiply the whole number part by the denominator and then add the numerator. The result is the new numerator, and the denominator remains the same.

For example, let's convert the mixed number 2492 \frac{4}{9} to an improper fraction.

  • Multiply the whole number part (2) by the denominator (9): 2×9=182 \times 9 = 18
  • Add the numerator (4) to the result: 18+4=2218 + 4 = 22
  • The new numerator is 22, and the denominator remains 9. So, the improper fraction is 229\frac{22}{9}.

Similarly, let's convert the mixed number 1291 \frac{2}{9} to an improper fraction.

  • Multiply the whole number part (1) by the denominator (9): 1×9=91 \times 9 = 9
  • Add the numerator (2) to the result: 9+2=119 + 2 = 11
  • The new numerator is 11, and the denominator remains 9. So, the improper fraction is 119\frac{11}{9}.

Step 2: Subtract the Fractions

Now that we have converted the mixed numbers to improper fractions, we can subtract the fractions.

229−119\frac{22}{9} - \frac{11}{9}

Since the denominators are the same, we can subtract the numerators directly.

22−119=119\frac{22 - 11}{9} = \frac{11}{9}

Step 3: Convert the Result Back to a Mixed Number

To convert the improper fraction 119\frac{11}{9} back to a mixed number, we need to divide the numerator (11) by the denominator (9).

11÷9=111 \div 9 = 1 with a remainder of 2

So, the mixed number is 1291 \frac{2}{9}.

Conclusion

In this article, we learned how to subtract mixed numbers and write the answer in simplest form. We followed a step-by-step process involving converting mixed numbers to improper fractions, subtracting the fractions, and then converting the result back to a mixed number. The final answer is 1291 \frac{2}{9}.

Example Problems

Problem 1

Subtract 3583 \frac{5}{8} from 2382 \frac{3}{8} and write the answer in simplest form.

Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert 3583 \frac{5}{8} to an improper fraction: (3×8)+58=24+58=298\frac{(3 \times 8) + 5}{8} = \frac{24 + 5}{8} = \frac{29}{8}
  • Convert 2382 \frac{3}{8} to an improper fraction: (2×8)+38=16+38=198\frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}

Step 2: Subtract the Fractions

298−198\frac{29}{8} - \frac{19}{8}

Since the denominators are the same, we can subtract the numerators directly.

29−198=108\frac{29 - 19}{8} = \frac{10}{8}

Step 3: Convert the Result Back to a Mixed Number

To convert the improper fraction 108\frac{10}{8} back to a mixed number, we need to divide the numerator (10) by the denominator (8).

10÷8=110 \div 8 = 1 with a remainder of 2

So, the mixed number is 1281 \frac{2}{8}.

Problem 2

Subtract 47124 \frac{7}{12} from 35123 \frac{5}{12} and write the answer in simplest form.

Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert 47124 \frac{7}{12} to an improper fraction: (4×12)+712=48+712=5512\frac{(4 \times 12) + 7}{12} = \frac{48 + 7}{12} = \frac{55}{12}
  • Convert 35123 \frac{5}{12} to an improper fraction: (3×12)+512=36+512=4112\frac{(3 \times 12) + 5}{12} = \frac{36 + 5}{12} = \frac{41}{12}

Step 2: Subtract the Fractions

5512−4112\frac{55}{12} - \frac{41}{12}

Since the denominators are the same, we can subtract the numerators directly.

55−4112=1412\frac{55 - 41}{12} = \frac{14}{12}

Step 3: Convert the Result Back to a Mixed Number

To convert the improper fraction 1412\frac{14}{12} back to a mixed number, we need to divide the numerator (14) by the denominator (12).

14÷12=114 \div 12 = 1 with a remainder of 2

So, the mixed number is 12121 \frac{2}{12}.

Final Answer

The final answer is 1291 \frac{2}{9}.

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Frequently Asked Questions

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. The result is the new numerator, and the denominator remains the same.

Q: How do I subtract mixed numbers?

A: To subtract mixed numbers, convert them to improper fractions, subtract the fractions, and then convert the result back to a mixed number.

Q: What if the denominators of the mixed numbers are different?

A: If the denominators are different, find the least common multiple (LCM) of the denominators, convert both mixed numbers to improper fractions with the LCM as the denominator, and then subtract the fractions.

Q: Can I subtract a mixed number from a whole number?

A: Yes, you can subtract a mixed number from a whole number by converting the whole number to a mixed number with a denominator of 1, subtracting the fractions, and then converting the result back to a mixed number.

Q: How do I simplify a mixed number?

A: To simplify a mixed number, divide the numerator by the denominator and write the result as a whole number and a remainder. The remainder becomes the new numerator, and the denominator remains the same.

Q: Can I add or multiply mixed numbers?

A: Yes, you can add or multiply mixed numbers by converting them to improper fractions, performing the operation, and then converting the result back to a mixed number.

Q: What if I have a negative mixed number?

A: A negative mixed number is a mixed number with a negative whole number part. To subtract a negative mixed number, convert it to a positive mixed number by changing the sign of the whole number part and then following the steps for subtracting mixed numbers.

Q: Can I have a mixed number with a negative fraction?

A: Yes, you can have a mixed number with a negative fraction. To subtract a mixed number with a negative fraction, convert it to an improper fraction, subtract the fractions, and then convert the result back to a mixed number.

Example Problems

Problem 1

Subtract 2342 \frac{3}{4} from 1241 \frac{2}{4} and write the answer in simplest form.

Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert 2342 \frac{3}{4} to an improper fraction: (2×4)+34=8+34=114\frac{(2 \times 4) + 3}{4} = \frac{8 + 3}{4} = \frac{11}{4}
  • Convert 1241 \frac{2}{4} to an improper fraction: (1×4)+24=4+24=64\frac{(1 \times 4) + 2}{4} = \frac{4 + 2}{4} = \frac{6}{4}

Step 2: Subtract the Fractions

114−64\frac{11}{4} - \frac{6}{4}

Since the denominators are the same, we can subtract the numerators directly.

11−64=54\frac{11 - 6}{4} = \frac{5}{4}

Step 3: Convert the Result Back to a Mixed Number

To convert the improper fraction 54\frac{5}{4} back to a mixed number, we need to divide the numerator (5) by the denominator (4).

5÷4=15 \div 4 = 1 with a remainder of 1

So, the mixed number is 1141 \frac{1}{4}.

Problem 2

Subtract 3783 \frac{7}{8} from 2382 \frac{3}{8} and write the answer in simplest form.

Step 1: Convert Mixed Numbers to Improper Fractions

  • Convert 3783 \frac{7}{8} to an improper fraction: (3×8)+78=24+78=318\frac{(3 \times 8) + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}
  • Convert 2382 \frac{3}{8} to an improper fraction: (2×8)+38=16+38=198\frac{(2 \times 8) + 3}{8} = \frac{16 + 3}{8} = \frac{19}{8}

Step 2: Subtract the Fractions

318−198\frac{31}{8} - \frac{19}{8}

Since the denominators are the same, we can subtract the numerators directly.

31−198=128\frac{31 - 19}{8} = \frac{12}{8}

Step 3: Convert the Result Back to a Mixed Number

To convert the improper fraction 128\frac{12}{8} back to a mixed number, we need to divide the numerator (12) by the denominator (8).

12÷8=112 \div 8 = 1 with a remainder of 4

So, the mixed number is 1481 \frac{4}{8}.

Final Answer

The final answer is 1141 \frac{1}{4}.