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2 years ago

What is is 1/4 + 9/10y -3/5y +7/8 written in simplest form?

Mathematics

2 answers:

svp [43]2 years ago

6 0

Answer:

3 • (4y + 15)

-----------------

Step-by-step explanation:

Long explanation get ready

STEP

Simplify —

Equation at the end of step

1 9 3 7

((—+(——•y))-(—•y))+—

4 10 5 8

STEP

Simplify —

Equation at the end of step

1 9 3 7

((—+(——•y))-(—•y))+—

4 10 5 8

STEP

Simplify ——

Equation at the end of step

1 9 3y 7

((— + (—— • y)) - ——) + —

4 10 5 8

STEP

Simplify —

Equation at the end of step

1 9y 3y 7

((— + ——) - ——) + —

4 10 5 8

STEP

Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple

The left denominator is : 4

The right denominator is : 10

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 2 1 2

5 0 1 1

Product of all

Prime Factors 4 10 20

Least Common Multiple:

Calculating Multipliers :

5.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. 5

—————————————————— = ——

L.C.M 20

R. Mult. • R. Num. 9y • 2

—————————————————— = ——————

L.C.M 20

Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

5 + 9y • 2 18y + 5

—————————— = ———————

20 20

Equation at the end of step

(18y + 5) 3y 7

(————————— - ——) + —

20 5 8

STEP

Calculating the Least Common Multiple :

6.1 Find the Least Common Multiple

The left denominator is : 20

The right denominator is : 5

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 2 0 2

5 1 1 1

Product of all

Prime Factors 20 5 20

Least Common Multiple:

Calculating Multipliers :

6.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 1

Right_M = L.C.M / R_Deno = 4

Making Equivalent Fractions :

6.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (18y+5)

—————————————————— = ———————

L.C.M 20

R. Mult. • R. Num. 3y • 4

—————————————————— = ——————

L.C.M 20

Adding fractions that have a common denominator :

6.4 Adding up the two equivalent fractions

(18y+5) - (3y • 4) 6y + 5

—————————————————— = ——————

20 20

Equation at the end of step

(6y + 5) 7

———————— + —

20 8

STEP

Calculating the Least Common Multiple :

7.1 Find the Least Common Multiple

The left denominator is : 20

The right denominator is : 8

Number of times each prime factor

appears in the factorization of:

Prime

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

2 2 3 3

5 1 0 1

Product of all

Prime Factors 20 8 40

Least Common Multiple:

Calculating Multipliers :

7.2 Calculate multipliers for the two fractions

Denote the Least Common Multiple by L.C.M

Denote the Left Multiplier by Left_M

Denote the Right Multiplier by Right_M

Denote the Left Deniminator by L_Deno

Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 2

Right_M = L.C.M / R_Deno = 5

Making Equivalent Fractions :

7.3 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (6y+5) • 2

—————————————————— = ——————————

L.C.M 40

R. Mult. • R. Num. 7 • 5

—————————————————— = —————

L.C.M 40

Adding fractions that have a common denominator :

7.4 Adding up the two equivalent fractions

(6y+5) • 2 + 7 • 5 12y + 45

—————————————————— = ————————

40 40

STEP

Pulling out like terms :

8.1 Pull out like factors :

12y + 45 = 3 • (4y + 15)

Leviafan [203]2 years ago

5 0

Answer:

Step-by-step explanation:

$\frac{1}{4}+\frac{9}{10}y - \frac{3}{5}y+\frac{7}{8}\\\\=\frac{1}{4}+\frac{7}{8}+\frac{9}{10}y-\frac{3}{5}y\\\\$

Combine like terms. 1/4 and 7/8 are like terms and LCD of 4 and 8 is 8

9/10y and -3/5y are like terms and LCD of 10 , 5 is 10

$= \frac{1*2}{4*2}+\frac{7}{8}+\frac{9}{10}y-\frac{3*2}{5*2}y\\\\=\frac{2}{8}+\frac{7}{8}+\frac{9}{10}y-\frac{6}{10}y\\\\=\frac{9}{8}+\frac{3}{10}y$

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