Certainly! Here's a clear and simple guide on how to solve problems involving fractions with whole numbers.
How to Solve Fractions with Whole Numbers
When you have a fraction and a whole number, you might be asked to add, subtract, multiply, or divide them. Here’s how to handle each operation:
1. Multiplying a Fraction by a Whole Number
Example: Multiply 34×5\frac{3}{4}\times 543×5 Steps:
- Convert the whole number to a fraction by putting it over 1: 5=515=\frac{5}{1}5=15
- Multiply the numerators: 3×5=153\times 5=153×5=15
- Multiply the denominators: 4×1=44\times 1=44×1=4
- So, 34×5=154\frac{3}{4}\times 5=\frac{15}{4}43×5=415
- Simplify or convert to a mixed number if needed: 154=334\frac{15}{4}=3\frac{3}{4}415=343
2. Dividing a Fraction by a Whole Number
Example: Divide 34÷5\frac{3}{4}\div 543÷5 Steps:
- Convert the whole number to a fraction: 5=515=\frac{5}{1}5=15
- Find the reciprocal of the whole number fraction: 15\frac{1}{5}51
- Multiply the fraction by the reciprocal: 34×15=320\frac{3}{4}\times \frac{1}{5}=\frac{3}{20}43×51=203
3. Adding a Fraction and a Whole Number
Example: Add 34+5\frac{3}{4}+543+5 Steps:
- Convert the whole number to a fraction with the same denominator: 5=5×44=2045=\frac{5\times 4}{4}=\frac{20}{4}5=45×4=420
- Add the numerators: 3+20=233+20=233+20=23
- Keep the denominator the same: 234\frac{23}{4}423
- Convert to mixed number if desired: 234=534\frac{23}{4}=5\frac{3}{4}423=543
4. Subtracting a Whole Number from a Fraction
Example: Subtract 5−345-\frac{3}{4}5−43 Steps:
- Convert the whole number to a fraction with the same denominator: 5=2045=\frac{20}{4}5=420
- Subtract the numerators: 20−3=1720-3=1720−3=17
- Keep the denominator the same: 174\frac{17}{4}417
- Convert to mixed number if desired: 174=414\frac{17}{4}=4\frac{1}{4}417=441
Summary Table
Operation| Method| Example Result
---|---|---
Multiply| Multiply numerator by whole number| 34×5=154\frac{3}{4}\times
5=\frac{15}{4}43×5=415
Divide| Multiply by reciprocal of whole number| 34÷5=320\frac{3}{4}\div
5=\frac{3}{20}43÷5=203
Add| Convert whole number to fraction, then add|
34+5=234\frac{3}{4}+5=\frac{23}{4}43+5=423
Subtract| Convert whole number to fraction, then subtract|
5−34=1745-\frac{3}{4}=\frac{17}{4}5−43=417
If you'd like, I can provide practice problems or explain any step in more detail!
