Math / Algebra

QuestionCalcula el término que ralta en cada proporcion. $\begin{array}{llrl} \frac{3}{6} & =\frac{11}{a} & \frac{2}{40} & =\frac{b}{60} \\ \frac{5}{35} & =\frac{c}{420} & \frac{6}{8} & =\frac{42}{d} \\ \frac{e}{8} & =\frac{35}{40} & \frac{2}{f} & =\frac{6}{42} \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to find the missing numbers in these fractions so that they are equivalent! Watch out! Don't flip the fractions around accidentally; keep the matching parts lined up correctly!

STEP 2

1. Solve for a
2. Solve for b
3. Solve for c
4. Solve for d
5. Solve for e
6. Solve for f

STEP 3

We have $\frac{3}{6} = \frac{11}{a}$ .
We want to find a.
Let's cross-multiply: $3 \cdot a = 6 \cdot 11$ .

STEP 4

So, $3a = 66$ .
Now, we want to isolate \textit{a}.
We can do this by dividing both sides by 3.
Remember, we're effectively dividing by one, since $\frac{3}{3} = 1$ , and multiplying by one doesn't change the value of the other side!

STEP 5

We get $a = \frac{66}{3} = 22$ .
So, $a = \textbf{22}$ !

STEP 6

We have $\frac{2}{40} = \frac{b}{60}$ . Cross-multiply: $2 \cdot 60 = 40 \cdot b$ , or $120 = 40b$ .

STEP 7

Divide both sides by 40 to isolate b: $b = \frac{120}{40} = 3$ .
So $b = \textbf{3}$ !

STEP 8

We have $\frac{5}{35} = \frac{c}{420}$ . Cross-multiply: $5 \cdot 420 = 35 \cdot c$ , or $2100 = 35c$ .

STEP 9

Divide both sides by 35 to get $c = \frac{2100}{35} = 60$ .
So $c = \textbf{60}$ !

STEP 10

We have $\frac{6}{8} = \frac{42}{d}$ . Cross-multiply: $6 \cdot d = 8 \cdot 42$ , or $6d = 336$ .

STEP 11

Divide both sides by 6: $d = \frac{336}{6} = 56$ .
Thus, $d = \textbf{56}$ !

STEP 12

We have $\frac{e}{8} = \frac{35}{40}$ . Cross-multiply: $e \cdot 40 = 8 \cdot 35$ , which simplifies to $40e = 280$ .

STEP 13

Divide both sides by 40: $e = \frac{280}{40} = 7$ .
So, $e = \textbf{7}$ !

STEP 14

We have $\frac{2}{f} = \frac{6}{42}$ . Cross-multiply: $2 \cdot 42 = 6 \cdot f$ , or $84 = 6f$ .

STEP 15

Divide both sides by 6: $f = \frac{84}{6} = 14$ .
Therefore, $f = \textbf{14}$ !

STEP 16

$a = 22$ , $b = 3$ , $c = 60$ , $d = 56$ , $e = 7$ , and $f = 14$ .

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QuestionCalcula el término que ralta en cada proporcion. $\begin{array}{llrl} \frac{3}{6} & =\frac{11}{a} & \frac{2}{40} & =\frac{b}{60} \\ \frac{5}{35} & =\frac{c}{420} & \frac{6}{8} & =\frac{42}{d} \\ \frac{e}{8} & =\frac{35}{40} & \frac{2}{f} & =\frac{6}{42} \end{array}$

Studdy Solution

STEP 1

What is this asking? We need to find the missing numbers in these fractions so that they are equivalent! Watch out! Don't flip the fractions around accidentally; keep the matching parts lined up correctly!

STEP 2

1. Solve for a
2. Solve for b
3. Solve for c
4. Solve for d
5. Solve for e
6. Solve for f

STEP 3

We have $\frac{3}{6} = \frac{11}{a}$ .
We want to find a.
Let's cross-multiply: $3 \cdot a = 6 \cdot 11$ .

STEP 4

So, $3a = 66$ .
Now, we want to isolate \textit{a}.
We can do this by dividing both sides by 3.
Remember, we're effectively dividing by one, since $\frac{3}{3} = 1$ , and multiplying by one doesn't change the value of the other side!

STEP 5

We get $a = \frac{66}{3} = 22$ .
So, $a = \textbf{22}$ !

STEP 6

We have $\frac{2}{40} = \frac{b}{60}$ . Cross-multiply: $2 \cdot 60 = 40 \cdot b$ , or $120 = 40b$ .

STEP 7

Divide both sides by 40 to isolate b: $b = \frac{120}{40} = 3$ .
So $b = \textbf{3}$ !

STEP 8

We have $\frac{5}{35} = \frac{c}{420}$ . Cross-multiply: $5 \cdot 420 = 35 \cdot c$ , or $2100 = 35c$ .

STEP 9

Divide both sides by 35 to get $c = \frac{2100}{35} = 60$ .
So $c = \textbf{60}$ !

STEP 10

We have $\frac{6}{8} = \frac{42}{d}$ . Cross-multiply: $6 \cdot d = 8 \cdot 42$ , or $6d = 336$ .

STEP 11

Divide both sides by 6: $d = \frac{336}{6} = 56$ .
Thus, $d = \textbf{56}$ !

STEP 12

We have $\frac{e}{8} = \frac{35}{40}$ . Cross-multiply: $e \cdot 40 = 8 \cdot 35$ , which simplifies to $40e = 280$ .

STEP 13

Divide both sides by 40: $e = \frac{280}{40} = 7$ .
So, $e = \textbf{7}$ !

STEP 14

We have $\frac{2}{f} = \frac{6}{42}$ . Cross-multiply: $2 \cdot 42 = 6 \cdot f$ , or $84 = 6f$ .

STEP 15

Divide both sides by 6: $f = \frac{84}{6} = 14$ .
Therefore, $f = \textbf{14}$ !

STEP 16

$a = 22$ , $b = 3$ , $c = 60$ , $d = 56$ , $e = 7$ , and $f = 14$ .

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Studdy Solution

STEP 1

What is this asking? We need to find the missing numbers in these fractions so that they are equivalent! Watch out! Don't flip the fractions around accidentally; keep the matching parts lined up correctly!

STEP 2

1. Solve for *a*2. Solve for *b*3. Solve for *c*4. Solve for *d*5. Solve for *e*6. Solve for *f*

STEP 3

We have 36=11a\frac{3}{6} = \frac{11}{a}63​=a11​.We want to find *a*.Let's **cross-multiply**: 3⋅a=6⋅113 \cdot a = 6 \cdot 113⋅a=6⋅11.

STEP 4

So, 3a=663a = 663a=66.Now, we want to **isolate** \textit{a}.We can do this by dividing both sides by **3**.Remember, we're effectively dividing by one, since 33=1\frac{3}{3} = 133​=1, and multiplying by one doesn't change the value of the other side!

STEP 5

We get a=663=22a = \frac{66}{3} = 22a=366​=22.So, a=22a = \textbf{22}a=22!

STEP 6

We have 240=b60\frac{2}{40} = \frac{b}{60}402​=60b​. **Cross-multiply**: 2⋅60=40⋅b2 \cdot 60 = 40 \cdot b2⋅60=40⋅b, or 120=40b120 = 40b120=40b.

STEP 7

**Divide both sides by 40** to isolate *b*: b=12040=3b = \frac{120}{40} = 3b=40120​=3.So b=3b = \textbf{3}b=3!

STEP 8

We have 535=c420\frac{5}{35} = \frac{c}{420}355​=420c​. **Cross-multiply**: 5⋅420=35⋅c5 \cdot 420 = 35 \cdot c5⋅420=35⋅c, or 2100=35c2100 = 35c2100=35c.

STEP 9

**Divide both sides by 35** to get c=210035=60c = \frac{2100}{35} = 60c=352100​=60.So c=60c = \textbf{60}c=60!

STEP 10

We have 68=42d\frac{6}{8} = \frac{42}{d}86​=d42​. **Cross-multiply**: 6⋅d=8⋅426 \cdot d = 8 \cdot 426⋅d=8⋅42, or 6d=3366d = 3366d=336.

STEP 11

**Divide both sides by 6**: d=3366=56d = \frac{336}{6} = 56d=6336​=56.Thus, d=56d = \textbf{56}d=56!

STEP 12

We have e8=3540\frac{e}{8} = \frac{35}{40}8e​=4035​. **Cross-multiply**: e⋅40=8⋅35e \cdot 40 = 8 \cdot 35e⋅40=8⋅35, which simplifies to 40e=28040e = 28040e=280.

STEP 13

**Divide both sides by 40**: e=28040=7e = \frac{280}{40} = 7e=40280​=7.So, e=7e = \textbf{7}e=7!

STEP 14

We have 2f=642\frac{2}{f} = \frac{6}{42}f2​=426​. **Cross-multiply**: 2⋅42=6⋅f2 \cdot 42 = 6 \cdot f2⋅42=6⋅f, or 84=6f84 = 6f84=6f.

STEP 15

**Divide both sides by 6**: f=846=14f = \frac{84}{6} = 14f=684​=14.Therefore, f=14f = \textbf{14}f=14!

STEP 16

a=22a = 22a=22, b=3b = 3b=3, c=60c = 60c=60, d=56d = 56d=56, e=7e = 7e=7, and f=14f = 14f=14.

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1. Solve for a
2. Solve for b
3. Solve for c
4. Solve for d
5. Solve for e
6. Solve for f

We have $\frac{3}{6} = \frac{11}{a}$ .
We want to find a.
Let's cross-multiply: $3 \cdot a = 6 \cdot 11$ .

So, $3a = 66$ .
Now, we want to isolate \textit{a}.
We can do this by dividing both sides by 3.
Remember, we're effectively dividing by one, since $\frac{3}{3} = 1$ , and multiplying by one doesn't change the value of the other side!

We get $a = \frac{66}{3} = 22$ .
So, $a = \textbf{22}$ !

We have $\frac{2}{40} = \frac{b}{60}$ . Cross-multiply: $2 \cdot 60 = 40 \cdot b$ , or $120 = 40b$ .

Divide both sides by 40 to isolate b: $b = \frac{120}{40} = 3$ .
So $b = \textbf{3}$ !

We have $\frac{5}{35} = \frac{c}{420}$ . Cross-multiply: $5 \cdot 420 = 35 \cdot c$ , or $2100 = 35c$ .

Divide both sides by 35 to get $c = \frac{2100}{35} = 60$ .
So $c = \textbf{60}$ !

We have $\frac{6}{8} = \frac{42}{d}$ . Cross-multiply: $6 \cdot d = 8 \cdot 42$ , or $6d = 336$ .

Divide both sides by 6: $d = \frac{336}{6} = 56$ .
Thus, $d = \textbf{56}$ !

We have $\frac{e}{8} = \frac{35}{40}$ . Cross-multiply: $e \cdot 40 = 8 \cdot 35$ , which simplifies to $40e = 280$ .

Divide both sides by 40: $e = \frac{280}{40} = 7$ .
So, $e = \textbf{7}$ !

We have $\frac{2}{f} = \frac{6}{42}$ . Cross-multiply: $2 \cdot 42 = 6 \cdot f$ , or $84 = 6f$ .

Divide both sides by 6: $f = \frac{84}{6} = 14$ .
Therefore, $f = \textbf{14}$ !

$a = 22$ , $b = 3$ , $c = 60$ , $d = 56$ , $e = 7$ , and $f = 14$ .