Which expressions are equivalent to the one below? Check all that apply. 21/7
The Correct Answer and Explanation is:
The expression given is 217\frac{21}{7}721. Let’s explore what equivalent expressions would be.
- Simplifying the expression: 217=3\frac{21}{7} = 3721=3 This is because 21÷7=321 \div 7 = 321÷7=3. So, 333 is an equivalent expression.
- Multiplication Form:
217\frac{21}{7}721 can also be written as a product using the reciprocal: 21×17=321 \times \frac{1}{7} = 321×71=3 This is another equivalent expression, as multiplying by the reciprocal of 7 gives the same result as dividing by 7. - Fraction Form with Equivalent Numerator and Denominator:
A fraction that has the same value but is expressed differently could be: 4214\frac{42}{14}1442 This is equivalent because: 4214=3(since 42÷14=3)\frac{42}{14} = 3 \quad \text{(since \( 42 \div 14 = 3 \))}1442=3(since 42÷14=3) This expression is also equivalent to 217\frac{21}{7}721. - Decimal Form:
Another way to express 217\frac{21}{7}721 is in decimal form: 3.03.03.0 Both 333 and 3.03.03.0 represent the same value, so this is another equivalent expression.
In conclusion, the following expressions are equivalent to 217\frac{21}{7}721:
- 333
- 21×1721 \times \frac{1}{7}21×71
- 4214\frac{42}{14}1442
- 3.03.03.0
All of these expressions result in the same value, 333, thus making them equivalent to the original expression.
