\( \sqrt{\frac{25}{16}}=\frac{5}{4}\) because the principal square root is positive. Take the root of both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is A. \( \frac{5}{4}\). \( \sqrt{\frac{25}{16}}=\frac{5}{4}\) because the principal square root is positive. Take the root of both numerator and denominator.
Step 3
Exam Tip
\( \sqrt{\frac{25}{16}}=\frac{5}{4}\) क्योंकि धनात्मक वर्गमूल लिया जाता है। भिन्न के वर्गमूल में अंश और हर दोनों का मूल लें।
Since \(2=\frac{8}{4}\), the interval from (0) to (2) has (8) fourth-parts and \(\frac{7}{4}\) is at the seventh part. Use the denominator to make equal units.
Step 2
Why this answer is correct
The correct answer is A. (8) भाग / (8) parts. Since \(2=\frac{8}{4}\), the interval from (0) to (2) has (8) fourth-parts and \(\frac{7}{4}\) is at the seventh part. Use the denominator to make equal units.
Step 3
Exam Tip
क्योंकि \(2=\frac{8}{4}\), इसलिए (0) से (2) तक (8) चौथाई भाग बनेंगे और \(\frac{7}{4}\) सातवें भाग पर होगा। हर को समान इकाई बनाने में प्रयोग करें।
The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). The midpoint of (0) and (1) is \(\frac{0+1}{2}=\frac{1}{2}\). To find a midpoint on a number line, take the average.
Step 3
Exam Tip
(0) और (1) का मध्य बिंदु \(\frac{0+1}{2}=\frac{1}{2}\) होता है। संख्या रेखा में मध्य निकालने के लिए औसत लें।
\(\frac{2}{5}=\frac{4}{10}\), so the distance is \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\). Use a common denominator before subtracting.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{3}{10}\). \(\frac{2}{5}=\frac{4}{10}\), so the distance is \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\). Use a common denominator before subtracting.
Step 3
Exam Tip
\(\frac{2}{5}=\frac{4}{10}\), इसलिए दूरी \(\frac{7}{10}-\frac{4}{10}=\frac{3}{10}\) है। समान हर बनाकर घटाएं।
The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{3}{5}\). The midpoint is \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\). To find the exact middle point, take the average of the two points.
Step 3
Exam Tip
मध्य संख्या \(\frac{\frac{2}{5}+\frac{4}{5}}{2}=\frac{3}{5}\) है। दो बिंदुओं के ठीक बीच के लिए उनका औसत लें।
\(\frac{11}{5}=2.2\), so it lies between (2) and (3). Convert an improper fraction to decimal or mixed form.
Step 2
Why this answer is correct
The correct answer is B. (2) और (3) / (2) and (3). \(\frac{11}{5}=2.2\), so it lies between (2) and (3). Convert an improper fraction to decimal or mixed form.
Step 3
Exam Tip
\(\frac{11}{5}=2.2\), इसलिए यह (2) और (3) के बीच है। अशुद्ध भिन्न को दशमलव या मिश्रित रूप में बदलें।
\(\frac{5}{8}\) means (5) parts out of (8) equal parts. Treat the denominator as divisions and the numerator as count.
Step 2
Why this answer is correct
The correct answer is C. (0) के बाद पांचवां बिंदु / Fifth point after (0). \(\frac{5}{8}\) means (5) parts out of (8) equal parts. Treat the denominator as divisions and the numerator as count.
Step 3
Exam Tip
\(\frac{5}{8}\) का अर्थ (8) बराबर भागों में से (5) भाग है। हर को भागों की संख्या और अंश को गिनती मानें।
\(-\frac{7}{4}=-1.75\), so it lies between (-2) and (-1). Be careful with direction for negative fractions.
Step 2
Why this answer is correct
The correct answer is A. (-2) और (-1) / (-2) and (-1). \(-\frac{7}{4}=-1.75\), so it lies between (-2) and (-1). Be careful with direction for negative fractions.
Step 3
Exam Tip
\(-\frac{7}{4}=-1.75\), इसलिए यह (-2) और (-1) के बीच होगा। ऋणात्मक भिन्न में दिशा को ध्यान से देखें।
\(0.333\ldots=\frac{1}{3}\) is a recurring decimal. Recurring decimals also represent fixed points on the number line.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{3}\). \(0.333\ldots=\frac{1}{3}\) is a recurring decimal. Recurring decimals also represent fixed points on the number line.
Step 3
Exam Tip
\(0.333\ldots=\frac{1}{3}\) एक आवर्ती दशमलव है। आवर्ती दशमलव भी संख्या रेखा पर निश्चित बिंदु दिखाते हैं।
\(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 2
Why this answer is correct
The correct answer is A. \(-\frac{3}{2}\). \(-\frac{3}{2}=-1.5\), so it lies between (-2) and (-1). For negative numbers, values increase to the right.
Step 3
Exam Tip
\(-\frac{3}{2}=-1.5\) होता है, इसलिए यह (-2) और (-1) के बीच है। ऋणात्मक संख्याओं में दाईं ओर जाने पर मान बढ़ता है।
The denominator contains (11) so the decimal will not terminate. Since it is rational it will be recurring.
Step 2
Why this answer is correct
The correct answer is A. अनवसानी आवर्ती / Non-terminating recurring. The denominator contains (11) so the decimal will not terminate. Since it is rational it will be recurring.
Step 3
Exam Tip
हर में (11) है इसलिए दशमलव समाप्त नहीं होगा। परिमेय संख्या होने के कारण यह आवर्ती होगा।
After simplification, (7) remains in the denominator, so the decimal is non-terminating recurring. In exams do not decide only from the original denominator.
Step 2
Why this answer is correct
The correct answer is A. अनवसानी आवर्ती / Non-terminating recurring. After simplification, (7) remains in the denominator, so the decimal is non-terminating recurring. In exams do not decide only from the original denominator.
Step 3
Exam Tip
सरलीकरण के बाद हर में (7) बचता है, इसलिए दशमलव अनवसानी आवर्ती होगा। परीक्षा में केवल मूल हर देखकर निर्णय न लें।
In \(\frac{63}{2^5\cdot5^2\cdot7}\), after cancelling (63) and (7), only (2) and (5) remain in the denominator. In exams reduce the fraction first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{63}{2^5\cdot5^2\cdot7}\). In \(\frac{63}{2^5\cdot5^2\cdot7}\), after cancelling (63) and (7), only (2) and (5) remain in the denominator. In exams reduce the fraction first.
Step 3
Exam Tip
\(\frac{63}{2^5\cdot5^2\cdot7}\) में (63) और (7) कटने के बाद हर में केवल (2) और (5) बचते हैं। परीक्षा में पहले भिन्न को सरलतम रूप में लाएं।
The denominator contains (7), so the decimal will not terminate and being rational it will recur. In exams decide after checking the denominator in lowest form.
Step 2
Why this answer is correct
The correct answer is A. अनवसानी आवर्ती / Non-terminating recurring. The denominator contains (7), so the decimal will not terminate and being rational it will recur. In exams decide after checking the denominator in lowest form.
Step 3
Exam Tip
हर में (7) है, इसलिए दशमलव समाप्त नहीं होगा और परिमेय होने से आवर्ती होगा। परीक्षा में हर को सरलतम रूप में देखकर निर्णय लें।
B. यह अनवसानी आवर्ती दशमलव है/It is non-terminating recurring decimal
Step 1
Concept
The denominator contains (13), and after simplification the denominator is not made only of (2) and (5). In exams always check prime factors of the denominator.
Step 2
Why this answer is correct
The correct answer is B. यह अनवसानी आवर्ती दशमलव है / It is non-terminating recurring decimal. The denominator contains (13), and after simplification the denominator is not made only of (2) and (5). In exams always check prime factors of the denominator.
Step 3
Exam Tip
हर में (13) है और भिन्न सरल करने पर भी केवल (2) और (5) नहीं बचते। परीक्षा में हर के अभाज्य गुणनखंड जरूर जांचें।
All numbers in the first set can be written in \(\frac{p}{q}\) form. The other sets contain an irrational number.
Step 2
Why this answer is correct
The correct answer is A. \({2,-5,0.4,\frac{7}{8}}\). All numbers in the first set can be written in \(\frac{p}{q}\) form. The other sets contain an irrational number.
Step 3
Exam Tip
पहले समूह की सभी संख्याएँ \(\frac{p}{q}\) रूप में लिखी जा सकती हैं। बाकी समूहों में अपरिमेय संख्या है।
