Summary of Expressions Equivalent to ( \frac{1}{4} + \frac{7}{8} )

Part A: Equivalent Expressions
To determine which expressions are equivalent to ( \frac{1}{4} + \frac{7}{8} ), we can analyze the options provided:

• Option 1: ( \frac{2}{8} + \frac{7}{8} )
  This simplifies to ( \frac{9}{8} ), which is not equivalent to ( \frac{1}{4} + \frac{7}{8} ).

• Option 2: ( \frac{4}{16} + \frac{15}{16} )
  This simplifies to ( \frac{19}{16} ), which is also not equivalent to ( \frac{1}{4} + \frac{7}{8} ).

• Option 3: ( \frac{8}{24} + \frac{21}{24} )
  This simplifies to ( \frac{29}{24} ), which is not equivalent.

• Option 4: ( \frac{7}{32} + \frac{28}{32} )
  This simplifies to ( \frac{35}{32} ), which does not match either.

• Option 5: ( \frac{10}{40} + \frac{35}{40} )
  This simplifies to ( \frac{45}{40} ), which is not equal to ( \frac{1}{4} + \frac{7}{8} ).

In conclusion, none of the provided options (2/8+7/8, 4/16+15/16, 8/24+21/24, 7/32+28/32, 10/40+35/40) are equivalent to ( \frac{1}{4} + \frac{7}{8} ).

Part B: Calculation of ( \frac{1}{4} + \frac{7}{8} )
Now, calculating ( \frac{1}{4} + \frac{7}{8} ):

1. The common denominator for these fractions is 8.
2. Rewrite ( \frac{1}{4} ) as ( \frac{2}{8} ).
3. Now add:
   [ \frac{2}{8} + \frac{7}{8} = \frac{9}{8} \text{ or } 1 \frac{1}{8} ]

Given the calculation, the only correct answer is ( 1 \frac{1}{8} ).

Links for Further Reference

1. BYJU'S Equivalent Expressions Calculator
2. Brainly Equivalent Expressions (Sample Problem)
3. SnapXam Equivalent Expressions Calculator
4. Calculatorsoup Equivalent Fractions
5. YouTube Lesson on Equivalent Expressions
6. Online Equivalent Expressions Calculator
7. Brainly Question on Equivalent Expressions

This summary provides both the analysis of expression equivalences and the calculation result for the given fractions.In Part A of the problem, you are asked to select all expressions that are equivalent to ( \frac{1}{4} + \frac{7}{8} ). The expressions provided for evaluation are:

1. ( \frac{2}{8} + \frac{7}{8} )
2. ( \frac{4}{16} + \frac{15}{16} )
3. ( \frac{8}{24} + \frac{21}{24} )
4. ( \frac{7}{32} + \frac{28}{32} )
5. ( \frac{10}{40} + \frac{35}{40} )

To determine which of these equations is equivalent to ( \frac{1}{4} + \frac{7}{8} ), we first need to find a common denominator in the original equation. The common denominator for ( \frac{1}{4} ) and ( \frac{7}{8} ) is 8. Therefore, ( \frac{1}{4} ) can be converted to ( \frac{2}{8} ). Thus:

[ \frac{1}{4} + \frac{7}{8} = \frac{2}{8} + \frac{7}{8} = \frac{9}{8} ]

Next, we can evaluate each of the provided expressions:

1. ( \frac{2}{8} + \frac{7}{8} = \frac{9}{8} ) (equivalent)
2. ( \frac{4}{16} + \frac{15}{16} = \frac{19}{16} ) (not equivalent)
3. ( \frac{8}{24} + \frac{21}{24} = \frac{29}{24} ) (not equivalent)
4. ( \frac{7}{32} + \frac{28}{32} = \frac{35}{32} ) (not equivalent)
5. ( \frac{10}{40} + \frac{35}{40} = \frac{45}{40} = \frac{9}{8} ) (equivalent)

Thus, the expressions that are equivalent to ( \frac{1}{4} + \frac{7}{8} ) are ( \frac{2}{8} + \frac{7}{8} ) and ( \frac{10}{40} + \frac{35}{40} ).

In Part B, you are asked to calculate the expression ( \frac{1}{4} + \frac{7}{8} ). As previously calculated, we found that the sum is:

[ \frac{1}{4} + \frac{7}{8} = \frac{9}{8} ]

This can also be expressed as a mixed number:

[ \frac{9}{8} = 1 \frac{1}{8} ]

From the choices presented, the correct answer is ( 1 \frac{1}{8} ).

In summary, for Part A, the equivalent expressions are ( \frac{2}{8} + \frac{7}{8} ) and ( \frac{10}{40} + \frac{35}{40} ). For Part B, the result of ( \frac{1}{4} + \frac{7}{8} ) is ( 1 \frac{1}{8} ).